Jawaban quiz bagi kelas S1TI-1M

Jawaban quiz bagi kelas S1TI-1M

  1. Silahkan menuliskan jawaban quiz di bagian komentar.
  2. Jangan lupa menuliskan nama dan NIM anda.
  3. Ingat perhatikan baik-baik kelas anda.

Perhatian : komentar tidak akan segera tertampil, menunggu disetujui terlebih dahulu.

105 Responses

  1. <?
    /*
    nama : lutfi hanif
    nim : 09.11.3507
    kelas : SI TI 3M
    */
    — mencari shuffle & contatination —

    echo "”;
    echo “”;
    echo “”;
    echo “lutfi hanif – 09.11.3507 – S1 TI 3M”;
    echo “”;
    echo “”;
    echo “”;
    echo ““;
    echo “Lutfi hanif”;
    echo “”;
    echo “09.11.3507”;
    echo “”;
    echo “S1 TI 3M”;
    echo “”;
    echo “
    “;
    echo “#########################”;
    echo “”;

    $proses = $_GET[‘proses’];
    $proses = $_POST[‘submit’];

    if(!isset($proses))
    {
    echo “”;
    echo “”;
    echo “”;
    echo “”;
    echo “masukkan kata pertama”;
    echo “”;
    echo “”;
    echo “”;
    echo “”;
    echo “”;
    echo “”;
    echo “”;
    echo “masukkan kata Kedua”;
    echo “”;
    echo “”;
    echo “”;
    echo “”;
    echo “”;
    echo “”;
    echo “”;
    echo “”;
    echo “”;
    echo ” “;
    echo “”;
    echo “”;
    echo “”;
    echo “”;
    }
    else
    {
    //memotong kata
    function potong ($konten, $kata)
    {
    $TMPNEWSPART = array();
    $TMP = explode(” “, $konten);

    for($i=0; $i < $kata; $i++)
    {
    $TMPNEWSPART[$i] = $TMP[$i];
    }
    $NEWSPART = implode(" ", $TMPNEWSPART);

    return $NEWSPART;
    }

    //memotong huruf
    function potong_kata ($kata, $huruf_ke)
    {
    $potong_kata = substr($kata, $huruf_ke, 1);
    return $potong_kata;
    }

    //mencari jumlah char
    \\function panjang_kata ($kata)
    {
    $panjang_kata = strlen ($kata);
    return $panjang_kata;
    }

    $kata1 = $_POST["kata1"];
    $kata2 = $_POST["kata2"];

    $kata_pertama = potong($kata1, 1);
    $kata_kedua = potong($kata2, 1);

    if ($kata1=='' or $kata2=='')
    {
    echo "Maaf, mungkin ada data yang belum anda masukkan!
    klik disini untuk mengulangi.
    “;
    }
    else
    {

    echo “”;
    echo “”;
    echo “”;
    echo “masukkan kata Pertama”;
    echo “”;
    echo “”;
    echo “:”;
    echo “”;
    echo “”;
    echo “$kata_pertama“;
    echo “”;
    echo “”;
    echo “”;
    echo “”;
    echo “masukkan Kata Kedua “;
    echo “”;
    echo “”;
    echo “:”;
    echo “”;
    echo “”;
    echo “$kata_kedua“;
    echo “”;
    echo “”;
    echo “”;
    echo “”;
    echo “Contanination”;
    echo “”;
    echo “”;
    echo “:”;
    echo “”;
    echo “”;
    echo “$kata_pertama$kata_kedua“;
    echo “”;
    echo “”;
    echo “”;
    echo “”;
    echo “Shuffle”;
    echo “”;
    echo “”;
    echo “:”;
    echo “”;
    echo “”;
    echo ““;

    $kata_pertama_mlai = 0;
    $kata_kedua_mlai = 0;

    $panjang_kata_1 = panjang_kata ($kata_pertama);
    $panjang_kata_2 = panjang_kata ($kata_kedua);

    if ( $panjang_kata_1 > $panjang_kata_2 )
    { $jml = $panjang_kata_1; }
    else
    { $jml = $panjang_kata_2; }

    for ( $x = 0; $x < $jml; $x++)
    {
    $kata_pertama_potong = potong_kata($kata_pertama, $kata_pertama_mlai);
    $kata_kedua_potong = potong_kata($kata_kedua,$kata_kedua_mlai);

    echo "$kata_pertama_potong";
    echo "$kata_kedua_potong";

    $kata_pertama_mlai = $kata_pertama_mlai + 1;
    $kata_kedua_mlai = $kata_kedua_mlai + 1;
    }

    echo "“;
    echo “”;
    echo “”;
    echo “”;

    echo “”;
    echo ”  “;
    echo “Untuk menjalankan program lagi klik disini.”;
    echo “”;
    echo “#################”;
    echo “”;
    echo “Terjadi kesalahan dalam menginputkan data..
    maka kata pertama yang dipakai
    “;
    echo “”;

    }
    }
    echo “”;
    echo “”;
    ?>

  2. Nama: Tiyas Tri Kusumawati
    NIM:10.11.4483
    KELAS: S1 TI 1M

    • 1. Example of antisymmetric matrix:
    0 1 -2
    A = -1 0 6
    2 -6 0
    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements.
    5 -2 8 0 -2 7
    A = 2 0 3 B = 2 0 6
    8 -2 4 -7 -6 0
    5 2 8 0 2 -7
    At = -2 0 -2Bt = -2 0 -6
    8 3 4 7 6 0
    -5 -2 -8 0 -2 7
    -At =2 -0 2 -Bt = 2 0 6
    -8 2 -4 -7 -6 0
    Kita bisa melihat bahwa A =-At dan B =-Bt. Jadi itu membuktikan bahwa antisimetrik matriks adalah matriks persegi dengan nol pada setiap elemen diagonal.
    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.
    0 -4 8 0 7 -3
    A = 4 0 -5 , B = -7 0 6
    -8 5 0 3 -6 0
    0+0 -4+7 8+(-3)
    C = A + B = 4+(-7) 0+0 -5+6
    -8+3 5+(-6) 0+0
    0 3 5
    = -3 0 1
    -5 -1 0
    0 -3 -5
    Ct = 3 0 -1
    5 1 0
    0 3 5
    -Ct = -3 0 1
    -5 -1 0
    C = -Ct (antisymmetric matrix)

  3. Nama : Ade Gunawan Mohamad Zainal Putra
    NIM : 10.11.4520
    Kelas : S1-TI 1M

    1. Example of antisymmetric matrix:

    0 3 -2
    A = -3 0 5
    2 -5 0

    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements.

    An antisymmetric matrix (skew-symmetric matrix) is a square matrix A whose transpose is also its negative; that is, it satisfies the equation A = −AT.

    Here are two examples of matrix, one with zero on each diagonal elements :
    7 -4 9 0 -4 9
    A = 4 2 8 B = 4 0 8
    -9 -8 5 -9 -8 0

    7 4 -9 0 4 -9
    At = -4 2 -8 Bt = -4 0 -8
    9 8 5 9 8 0

    -7 -4 9 0 -4 9
    -At = 4 -2 8 -Bt = 4 0 8
    -9 -8 -5 -9 -8 0

    We could see that A != -At and B = -Bt. So it’s proved that antisymmetric matrix is a square matrix with zero on each diagonal elements.

    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.

    0 -3 7 0 11 -5
    Let A = 3 0 -4 , B = -11 0 8
    -7 4 0 5 -8 0

    0+0 -3+11 7+(-5)
    C = A + B = 3+(-11) 0+0 -4+8
    -7+5 4+(-8) 0+0

    0 8 2
    = -8 0 4
    -2 -4 0

    0 -8 -2
    Ct = 8 0 -4
    2 4 0

    0 8 2
    -Ct = -8 0 4
    -2 -4 0

    C = -Ct (antisymmetric matrix)

  4. Nama: Punditya Derry Dwi Pratikno
    Nim: 10.11.4485
    Kelas: 1M
    a) the example of antisymmetric matrix
    [0,7,2;7,0,-3;-2,3,0]

    ans =

    0 7 2
    7 0 -3
    -2 3 0

    b) A= [0,-2,1;2,0,-3;-1,3,0]

    A =

    0 -2 1
    2 0 -3
    -1 3 0

    >> B = [3,5,7;-4,2,-1;9,-2,6]

    B =

    3 5 7
    -4 2 -1
    9 -2 6

    (A)transpose=

    0 2 -1
    -2 0 3
    1 -3 0

    (B)transpose=

    3 -4 9
    5 2 -2
    7 -1 6

    -(A)transpose=

    0 -2 1
    2 0 -3
    -1 3 0

    -(B)transpose=

    -3 4 -9
    -5 -2 2
    -7 1 6

    with that examples prove that -(A)transpose not equal to -(B)transpose

    c) A= [0,-1,2;1,0,-4;-2,4,-0]

    A =

    0 -1 2
    1 0 -4
    -2 4 0

    B= [0,-9,3;9,0,-7;-3,7,0]

    B =

    0 -9 3
    9 0 -7
    -3 7 0

    [A+B]

    ans =

    0 -10 5
    10 0 -11
    -5 11 0

    [A+B]transpose=

    0 10 -5
    -10 0 11
    5 -11 0

    -[A+B]transpose=

    0 -10 5
    10 0 -11
    -5 11 0

    in this case, prove that [A+B]=-[A+B]transpose

  5. Nama : Yonathan Prasetioso.
    NIM : 10.11.4517
    Kelas : S1 TI 1M

    a) Example of antisymmetric matrix:
    >> [0,-4,8;4,0,-7;-8,7,0]

    ans =

    0 -4 8
    4 0 -7
    -8 7 0

    b) Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements:
    >> A = [0,4,-2;-4,0,8;3,-8,0]

    A =

    0 4 -2
    -4 0 8
    3 -8 0

    >> B = [6,-4,8;-5,1,6;2,-4,0]

    B =

    6 -4 8
    -5 1 6
    2 -4 0

    >> (A)transpose

    0 4 3
    4 0 8
    2 -8 0

    >> (B)transpose

    -6 5 -2
    -4 -1 4
    8 -6 0

    >> -(A)transpose

    0 -4 2
    -4 0 -4
    -2 8 0

    >> -(B)transpose

    6 -5 2
    4 1 -4
    -8 6 0

    We could see that A != -At and B = -Bt. So it’s proved that antisymmetric matrix is a square matrix with zero on each diagonal elements.

    c) Prove that sum of two antisymmetric matrix is an antisymmetric matrix.
    >> A = [0,4,9;-4,0,5;-9,-5,0]

    A =

    0 4 9
    -4 0 5
    -9 -5 0

    >> B = [0,-3,8;3,0,-6;-8,6,0]

    B =

    0 -3 8
    3 0 -6
    -8 6 0

    >> [A+B]

    ans =

    0 1 17
    -1 0 -1
    -17 1 0

    >> [A+B]transpose

    0 -1 -17
    1 0 1
    17 -1 0

    >> -[A+B]transpose

    0 1 17
    -1 0 -1
    17 1 0

    Can be seen that the results of (A+B) equal to -(A+B)t.
    Then it can be written (A+B) = – (A+B)t.

  6. Nama : m. ulinnuha. n.h
    Kelas : 1M
    nim: 10.11.4544
    1. Example of antisymmetric matrix:

    0 4 -3
    A = -4 0 6
    3 -6 0

    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements.

    6 -3 8 0 -2 7
    A = 3 1 7 B = 2 0 6
    -8 -7 4 -7 -6 0

    6 3 -8 0 2 -7
    At = -3 1 -7 Bt = -2 0 -6
    8 7 4 7 6 0

    -6 -3 8 0 -2 7
    -At = 3 -1 7 -Bt = 2 0 6
    -8 -7 -4 -7 -6 0

    Kita bisa melihat bahwa A =-At dan B =-Bt. Jadi itu membuktikan bahwa antisimetrik matriks adalah matriks persegi dengan nol pada setiap elemen diagonal.

    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.

    0 -4 8 0 7 -3
    A = 4 0 -5 , B = -7 0 6
    -8 5 0 3 -6 0

    0+0 -4+7 8+(-3)
    C = A + B = 4+(-7) 0+0 -5+6
    -8+3 5+(-6) 0+0

    0 3 5
    = -3 0 1
    -5 -1 0

    0 -3 -5
    Ct = 3 0 -1
    5 1 0

    0 3 5
    -Ct = -3 0 1
    -5 -1 0

  7. Nama : muhammad ibrahim
    Nim : 10.11.4481
    Kelas : S1-TI-1M

    1. Example of antisymmetric matrix:

    0 4 -3
    A = -4 0 6
    3 -6 0

    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements.

    6 -3 8 0 -2 7
    A = 3 1 7 B = 2 0 6
    8 -7 4 -7 -6 0

    6 3 -8 0 2 -7
    At = -3 1 -7 Bt = -2 0 -6
    8 7 4 7 6 0

    -6 -3 8 0 -2 7
    -At = 3 -1 7 -Bt = 2 0 6
    -8 -7 -4 -7 -6 0

    Kita bisa melihat bahwa A =-At dan B =-Bt. Jadi itu membuktikan bahwa antisimetrik matriks adalah matriks persegi dengan nol pada setiap elemen diagonal.

    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.

    0 -4 8 0 7 -3
    A = 4 0 -5 , B = -7 0 6
    -8 5 0 3 -6 0

    0+0 -4+7 8+(-3)
    C = A + B = 4+(-7) 0+0 -5+6
    -8+3 5+(-6) 0+0

    0 3 5
    = -3 0 1
    -5 -1 0

    0 -3 -5
    Ct = 3 0 -1
    5 1 0

    0 3 5
    -Ct = -3 0 1
    -5 -1 0

  8. Nama : Hermawan Agus Prasetyo
    NIM : 10.11.4499
    Kelas : 1M

    1. Example of antisymmetric matrix:

    0 4 -3
    A = -4 0 6
    3 -6 0

    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements.

    6 -3 8 0 -2 7
    A = 3 1 7 B = 2 0 6
    8 -7 4 -7 -6 0

    6 3 -8 0 2 -7
    At = -3 1 -7 Bt = -2 0 -6
    8 7 4 7 6 0

    -6 -3 8 0 -2 7
    -At = 3 -1 7 -Bt = 2 0 6
    -8 -7 -4 -7 -6 0

    Kita bisa melihat bahwa A =-At dan B =-Bt. Jadi itu membuktikan bahwa antisimetrik matriks adalah matriks persegi dengan nol pada setiap elemen diagonal.

    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.

    0 -4 8 0 7 -3
    A = 4 0 -5 , B = -7 0 6
    -8 5 0 3 -6 0

    0+0 -4+7 8+(-3)
    C = A + B = 4+(-7) 0+0 -5+6
    -8+3 5+(-6) 0+0

    0 3 5
    = -3 0 1
    -5 -1 0

    0 -3 -5
    Ct = 3 0 -1
    5 1 0

    0 3 5
    -Ct = -3 0 1
    -5 -1 0

    C = -Ct (antisymmetric matrix)

  9. Nama : Jeri Wandana
    NIM : 10.11.4526

    1. Example of antisymmetric matrix
    >> A = [0 1 -2;-1 0 -2;2 2 0]

    A =

    0 1 -2
    -1 0 -2
    2 2 0

    >> -A

    ans =

    0 -1 2
    1 0 2
    -2 -2 0

    >> -A’

    ans =

    0 1 -2
    -1 0 -2
    2 2 0

    2. The sum of two antisymmetrics matrix
    >> B = [0 2 -1;-2 0 -4;1 4 0]

    B =

    0 2 -1
    -2 0 -4
    1 4 0
    >> A+B

    ans =

    0 3 -3
    -3 0 -6
    3 6 0

    >> -(A+B)

    ans =

    0 -3 3
    3 0 6
    -3 -6 0

    >> -(A+B)’

    ans =

    0 3 -3
    -3 0 -6
    3 6 0

    3. Antisymmetric matrix is a square matrix having diagonal element zero
    A =

    0 1 -2
    -1 0 -2
    2 2 0
    [0+0+0] = 0

  10. Nama : Punditya Derry Dwi Pratikno
    NIM : 10.11.4485
    Kelas : S1 TI 1M

    a) the example of antisymmetric matrix
    [0,7,2;7,0,-3;-2,3,0]

    ans =

    0 7 2
    7 0 -3
    -2 3 0

    b) A= [0,-2,1;2,0,-3;-1,3,0]

    A =

    0 -2 1
    2 0 -3
    -1 3 0

    >> B = [3,5,7;-4,2,-1;9,-2,6]

    B =

    3 5 7
    -4 2 -1
    9 -2 6

    (A)transpose=

    0 2 -1
    -2 0 3
    1 -3 0

    (B)transpose=

    3 -4 9
    5 2 -2
    7 -1 6

    -(A)transpose=

    0 -2 1
    2 0 -3
    -1 3 0

    -(B)transpose=

    -3 4 -9
    -5 -2 2
    -7 1 6

    with that examples prove that -(A)transpose not equal to -(B)transpose

    c) A= [0,-1,2;1,0,-4;-2,4,-0]

    A =

    0 -1 2
    1 0 -4
    -2 4 0

    B= [0,-9,3;9,0,-7;-3,7,0]

    B =

    0 -9 3
    9 0 -7
    -3 7 0

    [A+B]

    ans =

    0 -10 5
    10 0 -11
    -5 11 0

    [A+B]transpose=

    0 10 -5
    -10 0 11
    5 -11 0

    -[A+B]transpose=

    0 -10 5
    10 0 -11
    -5 11 0

    in this case, prove that [A+B]=-[A+B]transpose

  11. Nama : Punditya Derry Dwi Pratikno
    NIM : 10.11.4485
    Kelas : S1 TI 1M
    a) the example of antisymmetric matrix
    [0,7,2;7,0,-3;-2,3,0]

    ans =

    0 7 2
    7 0 -3
    -2 3 0

    b) A= [0,-2,1;2,0,-3;-1,3,0]

    A =

    0 -2 1
    2 0 -3
    -1 3 0

    >> B = [3,5,7;-4,2,-1;9,-2,6]

    B =

    3 5 7
    -4 2 -1
    9 -2 6

    (A)transpose=

    0 2 -1
    -2 0 3
    1 -3 0

    (B)transpose=

    3 -4 9
    5 2 -2
    7 -1 6

    -(A)transpose=

    0 -2 1
    2 0 -3
    -1 3 0

    -(B)transpose=

    -3 4 -9
    -5 -2 2
    -7 1 6

    with that examples prove that -(A)transpose not equal to -(B)transpose

    c) A= [0,-1,2;1,0,-4;-2,4,-0]

    A =

    0 -1 2
    1 0 -4
    -2 4 0

    B= [0,-9,3;9,0,-7;-3,7,0]

    B =

    0 -9 3
    9 0 -7
    -3 7 0

    [A+B]

    ans =

    0 -10 5
    10 0 -11
    -5 11 0

    [A+B]transpose=

    0 10 -5
    -10 0 11
    5 -11 0

    -[A+B]transpose=

    0 -10 5
    10 0 -11
    -5 11 0

    in this case, prove that [A+B]=-[A+B]transpose

  12. Nama : M. ulinuha
    NIM : 10.11.4544
    Kelas : 1M

    1. Example of antisymmetric matrix:

    0 4 -3
    A = -4 0 6
    3 -6 0

    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements.

    6 -3 8 0 -2 7
    A = 3 1 7 B = 2 0 6
    8 -7 4 -7 -6 0

    6 3 -8 0 2 -7
    At = -3 1 -7 Bt = -2 0 -6
    8 7 4 7 6 0

    -6 -3 8 0 -2 7
    -At = 3 -1 7 -Bt = 2 0 6
    -8 -7 -4 -7 -6 0

    Kita bisa melihat bahwa A =-At dan B =-Bt. Jadi itu membuktikan bahwa antisimetrik matriks adalah matriks persegi dengan nol pada setiap elemen diagonal.

    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.

    0 -4 8 0 7 -3
    A = 4 0 -5 , B = -7 0 6
    -8 5 0 3 -6 0

    0+0 -4+7 8+(-3)
    C = A + B = 4+(-7) 0+0 -5+6
    -8+3 5+(-6) 0+0

    0 3 5
    = -3 0 1
    -5 -1 0

    0 -3 -5
    Ct = 3 0 -1
    5 1 0

    0 3 5
    -Ct = -3 0 1
    -5 -1 0

  13. nama : rizal wahyudin
    nim : 10.11.4534
    kelas : s1 TI 1m

    1. Example of antisymmetric matrix:
    >> A=[0 -2 -1;-2 0 3;1 -3 0]
    A =
    0 -2 -1
    -2 0 3
    1 -3 0
    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements:
    >> A=[6 -3 8;3 1 7;-8 -7 4],B=[0 -3 8;3 0 7;-8 -7 0]
    A =
    6 -3 8
    3 1 7
    -8 -7 4
    B =
    0 -3 8
    3 0 7
    -8 -7 0
    >> A’,B’
    ans =
    6 3 -8
    -3 1 -7
    8 7 4
    ans =
    0 3 -8
    -3 0 -7
    8 7 0
    >> -A’,-B’
    ans =
    -6 -3 8
    3 -1 7
    -8 -7 -4
    ans =
    0 -3 8
    3 0 7
    -8 -7 0
    Kita bisa lihat bahwa A =-At dan B =-Bt. Jadi itu dapat di buktikan bahwa antisimetrik matriks adalah matriks persegi dengan nol pada setiap elemen diagonal.
    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.
    >> A=[0 -4 8;4 0 -5;-8 5 0],B=[0 7 -3;-7 0 6;3 -6 0]
    A =
    0 -4 8
    4 0 -5
    -8 5 0
    B =
    0 7 -3
    -7 0 6
    3 -6 0
    >> C=A+B
    C =
    0 3 5
    -3 0 1
    -5 -1 0
    >> C’
    ans =
    0 -3 -5
    3 0 -1
    5 1 0
    >> -C’
    ans =
    0 3 5
    -3 0 1
    -5 -1 0
    C = -Ct (antisymmetric matrix berarti benar)

  14. Nama : muhammad ibrahim
    NIM : 10.11.4481
    Kelas : 1M

    1. Example of antisymmetric matrix:

    0 4 -3
    A = -4 0 6
    3 -6 0

    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements.

    6 -3 8 0 -2 7
    A = 3 1 7 B = 2 0 6
    8 -7 4 -7 -6 0

    6 3 -8 0 2 -7
    At = -3 1 -7 Bt = -2 0 -6
    8 7 4 7 6 0

    -6 -3 8 0 -2 7
    -At = 3 -1 7 -Bt = 2 0 6
    -8 -7 -4 -7 -6 0

    Kita bisa melihat bahwa A =-At dan B =-Bt. Jadi itu membuktikan bahwa antisimetrik matriks adalah matriks persegi dengan nol pada setiap elemen diagonal.

    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.

    0 -4 8 0 7 -3
    A = 4 0 -5 , B = -7 0 6
    -8 5 0 3 -6 0

    0+0 -4+7 8+(-3)
    C = A + B = 4+(-7) 0+0 -5+6
    -8+3 5+(-6) 0+0

    0 3 5
    = -3 0 1
    -5 -1 0

    0 -3 -5
    Ct = 3 0 -1
    5 1 0

    0 3 5
    -Ct = -3 0 1
    -5 -1 0

  15. nama : rizal wahyudin
    nim : 10.11.4534
    kelas : s1 TI 1m

    1. Example of antisymmetric matrix:
    >> A=[0 -2 -1;-2 0 3;1 -3 0]
    A =
    0 -2 -1
    -2 0 3
    1 -3 0
    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements:
    >> A=[6 -3 8;3 1 7;-8 -7 4],B=[0 -3 8;3 0 7;-8 -7 0]
    A =
    6 -3 8
    3 1 7
    -8 -7 4
    B =
    0 -3 8
    3 0 7
    -8 -7 0
    >> A’,B’
    ans =
    6 3 -8
    -3 1 -7
    8 7 4
    ans =
    0 3 -8
    -3 0 -7
    8 7 0
    >> -A’,-B’
    ans =
    -6 -3 8
    3 -1 7
    -8 -7 -4
    ans =
    0 -3 8
    3 0 7
    -8 -7 0

    Kita bisa lihat bahwa A =-At dan B =-Bt. Jadi itu dapat di buktikan bahwa antisimetrik matriks adalah matriks persegi dengan nol pada setiap elemen diagonal.
    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.
    >> A=[0 -4 8;4 0 -5;-8 5 0],B=[0 7 -3;-7 0 6;3 -6 0]
    A =
    0 -4 8
    4 0 -5
    -8 5 0
    B =
    0 7 -3
    -7 0 6
    3 -6 0
    >> C=A+B
    C =
    0 3 5
    -3 0 1
    -5 -1 0
    >> C’
    ans =
    0 -3 -5
    3 0 -1
    5 1 0
    >> -C’
    ans =
    0 3 5
    -3 0 1
    -5 -1 0
    C = -Ct (antisymmetric matrix berarti benar)

  16. Nama : m.ulinnuha
    NIM : 10.11.4544
    Kelas : 1M

    1. Example of antisymmetric matrix:

    0 4 -3
    A = -4 0 6
    3 -6 0

    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements.

    6 -3 8 0 -2 7
    A = 3 1 7 B = 2 0 6
    8 -7 4 -7 -6 0

    6 3 -8 0 2 -7
    At = -3 1 -7 Bt = -2 0 -6
    8 7 4 7 6 0

    -6 -3 8 0 -2 7
    -At = 3 -1 7 -Bt = 2 0 6
    -8 -7 -4 -7 -6 0

    Kita bisa melihat bahwa A =-At dan B =-Bt. Jadi itu membuktikan bahwa antisimetrik matriks adalah matriks persegi dengan nol pada setiap elemen diagonal.

    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.

    0 -4 8 0 7 -3
    A = 4 0 -5 , B = -7 0 6
    -8 5 0 3 -6 0

    0+0 -4+7 8+(-3)
    C = A + B = 4+(-7) 0+0 -5+6
    -8+3 5+(-6) 0+0

    0 3 5
    = -3 0 1
    -5 -1 0

    0 -3 -5
    Ct = 3 0 -1
    5 1 0

    0 3 5
    -Ct = -3 0 1
    -5 -1 0

  17. Nama : M. Ulinuha N.H
    NIM : 10.11.4544
    Kelas : 1M

    1. Example of antisymmetric matrix:

    0 4 -3
    A = -4 0 6
    3 -6 0

    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements.

    6 -3 8 0 -2 7
    A = 3 1 7 B = 2 0 6
    8 -7 4 -7 -6 0

    6 3 -8 0 2 -7
    At = -3 1 -7 Bt = -2 0 -6
    8 7 4 7 6 0

    -6 -3 8 0 -2 7
    -At = 3 -1 7 -Bt = 2 0 6
    -8 -7 -4 -7 -6 0

    Kita bisa melihat bahwa A =-At dan B =-Bt. Jadi itu membuktikan bahwa antisimetrik matriks adalah matriks persegi dengan nol pada setiap elemen diagonal.

    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.

    0 -4 8 0 7 -3
    A = 4 0 -5 , B = -7 0 6
    -8 5 0 3 -6 0

    0+0 -4+7 8+(-3)
    C = A + B = 4+(-7) 0+0 -5+6
    -8+3 5+(-6) 0+0

    0 3 5
    = -3 0 1
    -5 -1 0

    0 -3 -5
    Ct = 3 0 -1
    5 1 0

    0 3 5
    -Ct = -3 0 1
    -5 -1 0

  18. NAMA : RIZAL WAHYUDIN
    NIM : 10.11.4534
    KELAS : S1 TI 1M

    1. Example of antisymmetric matrix:
    >> A=[0 -2 -1;-2 0 3;1 -3 0]
    A =
    0 -2 -1
    -2 0 3
    1 -3 0
    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements:
    >> A=[6 -3 8;3 1 7;-8 -7 4],B=[0 -3 8;3 0 7;-8 -7 0]
    A =
    6 -3 8
    3 1 7
    -8 -7 4
    B =
    0 -3 8
    3 0 7
    -8 -7 0
    >> A’,B’
    ans =
    6 3 -8
    -3 1 -7
    8 7 4
    ans =
    0 3 -8
    -3 0 -7
    8 7 0
    >> -A’,-B’
    ans =
    -6 -3 8
    3 -1 7
    -8 -7 -4
    ans =
    0 -3 8
    3 0 7
    -8 -7 0
    Kita bisa melihat bahwa A =-At dan B =-Bt. Jadi itu membuktikan bahwa antisimetrik matriks adalah matriks persegi dengan nol pada setiap elemen diagonal.
    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.
    >> A=[0 -4 8;4 0 -5;-8 5 0],B=[0 7 -3;-7 0 6;3 -6 0]
    A =
    0 -4 8
    4 0 -5
    -8 5 0
    B =
    0 7 -3
    -7 0 6
    3 -6 0
    >> C=A+B
    C =
    0 3 5
    -3 0 1
    -5 -1 0
    >> C’
    ans =
    0 -3 -5
    3 0 -1
    5 1 0
    >> -C’
    ans =
    0 3 5
    -3 0 1
    -5 -1 0
    C = -Ct (antisymmetric matrix berarti benar)

  19. NAMA : RIZAL WAHYUDIN
    NIM : 10.11.4534
    KELAS : S1 TI 1M

    1. Example of antisymmetric matrix:
    >> A=[0 -2 -1;-2 0 3;1 -3 0]
    A =
    0 -2 -1
    -2 0 3
    1 -3 0
    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements:
    >> A=[6 -3 8;3 1 7;-8 -7 4],B=[0 -3 8;3 0 7;-8 -7 0]
    A =
    6 -3 8
    3 1 7
    -8 -7 4
    B =
    0 -3 8
    3 0 7
    -8 -7 0
    >> A’,B’
    ans =
    6 3 -8
    -3 1 -7
    8 7 4
    ans =
    0 3 -8
    -3 0 -7
    8 7 0
    >> -A’,-B’
    ans =
    -6 -3 8
    3 -1 7
    -8 -7 -4
    ans =
    0 -3 8
    3 0 7
    -8 -7 0
    Kita bisa melihat bahwa A =-At dan B =-Bt. Jadi itu membuktikan bahwa antisimetrik matriks adalah matriks persegi dengan nol pada setiap elemen diagonal.
    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.
    >> A=[0 -4 8;4 0 -5;-8 5 0],B=[0 7 -3;-7 0 6;3 -6 0]
    A =
    0 -4 8
    4 0 -5
    -8 5 0
    B =
    0 7 -3
    -7 0 6
    3 -6 0
    >> C=A+B
    C =
    0 3 5
    -3 0 1
    -5 -1 0
    >> C’
    ans =
    0 -3 -5
    3 0 -1
    5 1 0
    >> -C’
    ans =
    0 3 5
    -3 0 1
    -5 -1 0
    C = -Ct (antisymmetric matrix berarti benar)

  20. nama : deded fandilah
    nim : 10.11.4515
    kelas : S1 TI M

    1. Example of antisymmetric matrix:

    0 4 -3
    A = -4 0 6
    3 -6 0

    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements.

    6 -3 8 0 -2 7
    A = 3 1 7 B = 2 0 6
    8 -7 4 -7 -6 0

    6 3 -8 0 2 -7
    At = -3 1 -7 Bt = -2 0 -6
    8 7 4 7 6 0

    -6 -3 8 0 -2 7
    -At = 3 -1 7 -Bt = 2 0 6
    -8 -7 -4 -7 -6 0

    Kita bisa melihat bahwa A =-At dan B =-Bt. Jadi itu membuktikan bahwa antisimetrik matriks adalah matriks persegi dengan nol pada setiap elemen diagonal.

    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.

    0 -4 8 0 7 -3
    A = 4 0 -5 , B = -7 0 6
    -8 5 0 3 -6 0

    0+0 -4+7 8+(-3)
    C = A + B = 4+(-7) 0+0 -5+6
    -8+3 5+(-6) 0+0

    0 3 5
    = -3 0 1
    -5 -1 0

    0 -3 -5
    Ct = 3 0 -1
    5 1 0

    0 3 5
    -Ct = -3 0 1
    -5 -1 0

    C = -Ct (antisymmetric matrix)

  21. Nama: Rizky Aprio Prasetyo
    NIM: 10.11.4496
    Kelas: TI 1M

    1. Example of antisymmetric matrix:

    0 4 -2
    A = -3 2 5
    1 -5 0

    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements.

    Antisymmetric matrix is an anti of symmetric matrix, with (A= -At ). That mean the matrix is equal to its transpose, but each element of the transposed matrix has an opposite sign of the matrix.

    Here are two examples of symmetric matrix, one with zero on each diagonal elements.

    6 -2 1 6 5 9
    A = 4 2 5 B = -2 0 -1
    -8 -3 2 1 -4 2

    -6 2 1 -6 -5 -9
    At = -4 -2 -5 Bt = 2 0 1
    8 3 -2 -1 4 -2

    6 -2 1 6 5 9
    -At = 4 2 5 -Bt = -2 0 -1
    -8 -3 2 1 -4 2

    We could see that A != -At and B = -Bt. So it’s proved that antisymmetric matrix is a square matrix with zero on each diagonal elements.

    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.

    1 2 1 4 -2 -5
    Let A = 3 0 3 , B = -1 0 4
    -2 3 0 5 -4 0

    1+4 2+(-2) 1+(-5)
    C = A + B = 3+(-1) 0+0 3+4
    -2+5 3+(-4) 0+0

    5 0 -4
    = 2 0 7
    3 -1 0

    5 0 -4
    Ct = 2 0 7
    3 -1 0

    -5 0 4
    -Ct = -2 0 -7
    -3 1 0

    C = -Ct (antisymmetric matrix)

  22. Nama : Ibnu Priharyanto
    NIM : 10.21.0489

    1).jawaban soal A

    >> A=[5 6 7;7 6 5;6 7 5]

    A =

    5 6 7
    7 6 5
    6 7 5

    >> -A’

    ans =

    -5 -7 -6
    -6 -6 -7
    -7 -5 -5

    2).Jawaban Soal B

    >>A=[0 -2 -1;-2 0 3;1 -3 0]

    A =

    0 -2 -1
    -2 0 3
    1 -3 0

    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements:

    >> A=[6 -3 8;3 1 7;-8 -7 4],B=[0 -3 8;3 0 7;-8 -7 0]

    A =

    6 -3 8
    3 1 7
    -8 -7 4

    B =

    0 -3 8
    3 0 7
    -8 -7 0

    >> A’,B’

    ans =

    6 3 -8
    -3 1 -7
    8 7 4

    ans =

    0 3 -8
    -3 0 -7
    8 7 0

    >> -A’,-B’

    ans =

    -6 -3 8
    3 -1 7
    -8 -7 -4

    ans =

    0 -3 8
    3 0 7
    -8 -7 0

    Kita bisa melihat bahwa A =-At dan B =-Bt. Jadi itu membuktikan bahwa antisimetrik matriks adalah matriks persegi dengan nol pada setiap elemen diagonal.

    3).Jawaban Soal C

    >> A=[0 -4 8;4 0 -5;-8 5 0],B=[0 7 -3;-7 0 6;3 -6 0]

    A =

    0 -4 8
    4 0 -5
    -8 5 0

    B =

    0 7 -3
    -7 0 6
    3 -6 0

    >> C=A+B

    C =

    0 3 5
    -3 0 1
    -5 -1 0

    >> C’

    ans =

    0 -3 -5
    3 0 -1
    5 1 0

    >> -C’

    ans =

    0 3 5
    -3 0 1
    -5 -1 0

    C = -Ct (antisymmetric matrix)

  23. Nama :Ngadiyanto
    NIM : 10.21.0487

    1).jawaban soal A

    >> A=[7 8 9;9 8 7;8 9 7]

    A =

    7 8 9
    9 8 7
    8 9 7

    >> -A’

    ans =

    -7 -9 -8
    -8 -7 -9
    -9 -7 -7

    2).Jawaban Soal B

    >>A=[0 -2 -1;-2 0 3;1 -3 0]

    A =

    0 -2 -1
    -2 0 3
    1 -3 0

    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements:

    >> A=[6 -3 8;3 1 7;-8 -7 4],B=[0 -3 8;3 0 7;-8 -7 0]

    A =

    6 -3 8
    3 1 7
    -8 -7 4

    B =

    0 -3 8
    3 0 7
    -8 -7 0

    >> A’,B’

    ans =

    6 3 -8
    -3 1 -7
    8 7 4

    ans =

    0 3 -8
    -3 0 -7
    8 7 0

    >> -A’,-B’

    ans =

    -6 -3 8
    3 -1 7
    -8 -7 -4

    ans =

    0 -3 8
    3 0 7
    -8 -7 0

    Kita bisa melihat bahwa A =-At dan B =-Bt. Jadi itu membuktikan bahwa antisimetrik matriks adalah matriks persegi dengan nol pada setiap elemen diagonal.

    3).Jawaban Soal C

    >> A=[0 -4 8;4 0 -5;-8 5 0],B=[0 7 -3;-7 0 6;3 -6 0]

    A =

    0 -4 8
    4 0 -5
    -8 5 0

    B =

    0 7 -3
    -7 0 6
    3 -6 0

    >> C=A+B

    C =

    0 3 5
    -3 0 1
    -5 -1 0

    >> C’

    ans =

    0 -3 -5
    3 0 -1
    5 1 0

    >> -C’

    ans =

    0 3 5
    -3 0 1
    -5 -1 0

    C = -Ct (antisymmetric matrix)

  24. Nama : Oky Klinston Tambun
    NIM : 10.11.4494
    Kelas : S1 TI 1M

    1. Example of antisymmetric matrix:
    A = 0 1 5
    -1 0 -6
    -5 6 0

    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements:
    A = 0 5 -9
    -5 0 3
    9 -3 0

    At = 0 -5 9
    5 0 -3
    -9 3 0

    -At = 0 5 -9
    -5 0 3
    -9 -3 0

    B = 5 0 4
    -6 2 7
    2 3 8

    Bt = 5 -6 2
    0 2 3
    4 7 8

    -Bt = -5 6 -2
    0 -2 -3
    -4 -7 -8

    Terbukti bahwa -At mempunyai diagonal nol. Maka antisymetric -At mempunyai diagonal matrik.

    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.
    A = 0 1 -3
    -1 0 6
    3 -6 0

    B = 0 -2 4
    2 0 -7
    -4 7 0

    C = 0 -1 1
    1 0 -1
    -1 1 0

    Ct = 0 1 -1
    -1 0 1
    1 -1 0

    -Ct = 0 -1 1
    1 0 -1
    -1 1 0

    terbukti C = – Ct.

  25. nama : febrian budi utama
    nim : 10.11.4543
    kls : S1 TI 1M

    1. Example of antisymmetric matrix:
    >> A=[0 -2 -1;-2 0 3;1 -3 0]
    A =
    0 -2 -1
    -2 0 3
    1 -3 0
    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements:
    >> A=[6 -3 8;3 1 7;-8 -7 4],B=[0 -3 8;3 0 7;-8 -7 0]
    A =
    6 -3 8
    3 1 7
    -8 -7 4
    B =
    0 -3 8
    3 0 7
    -8 -7 0
    >> A’,B’
    ans =
    6 3 -8
    -3 1 -7
    8 7 4
    ans =
    0 3 -8
    -3 0 -7
    8 7 0
    >> -A’,-B’
    ans =
    -6 -3 8
    3 -1 7
    -8 -7 -4
    ans =
    0 -3 8
    3 0 7
    -8 -7 0
    Kita bisa melihat bahwa A =-At dan B =-Bt. Jadi itu membuktikan bahwa antisimetrik matriks adalah matriks persegi dengan nol pada setiap elemen diagonal.
    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.
    >> A=[0 -4 8;4 0 -5;-8 5 0],B=[0 7 -3;-7 0 6;3 -6 0]
    A =
    0 -4 8
    4 0 -5
    -8 5 0
    B =
    0 7 -3
    -7 0 6
    3 -6 0
    >> C=A+B
    C =
    0 3 5
    -3 0 1
    -5 -1 0
    >> C’
    ans =
    0 -3 -5
    3 0 -1
    5 1 0
    >> -C’
    ans =
    0 3 5
    -3 0 1
    -5 -1 0
    C = -Ct (antisymmetric matrix berarti benar)

  26. NAMA : Pandu Yudistira Nugraha
    NIM : 10.11.4508
    KELAS : S1 TI 1M

    1. Example of antisymmetric matrix:
    >> A=[0 -2 -1;-2 0 3;1 -3 0]
    A =
    0 -2 -1
    -2 0 3
    1 -3 0
    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements:
    >> A=[6 -3 8;3 1 7;-8 -7 4],B=[0 -3 8;3 0 7;-8 -7 0]
    A =
    6 -3 8
    3 1 7
    -8 -7 4
    B =
    0 -3 8
    3 0 7
    -8 -7 0
    >> A’,B’
    ans =
    6 3 -8
    -3 1 -7
    8 7 4
    ans =
    0 3 -8
    -3 0 -7
    8 7 0
    >> -A’,-B’
    ans =
    -6 -3 8
    3 -1 7
    -8 -7 -4
    ans =
    0 -3 8
    3 0 7
    -8 -7 0
    Kita bisa melihat bahwa A =-At dan B =-Bt. Jadi itu membuktikan bahwa antisimetrik matriks adalah matriks persegi dengan nol pada setiap elemen diagonal.
    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.
    >> A=[0 -4 8;4 0 -5;-8 5 0],B=[0 7 -3;-7 0 6;3 -6 0]
    A =
    0 -4 8
    4 0 -5
    -8 5 0
    B =
    0 7 -3
    -7 0 6
    3 -6 0
    >> C=A+B
    C =
    0 3 5
    -3 0 1
    -5 -1 0
    >> C’
    ans =
    0 -3 -5
    3 0 -1
    5 1 0
    >> -C’
    ans =
    0 3 5
    -3 0 1
    -5 -1 0
    C = -Ct (antisymmetric matrix berarti benar)

  27. Nama : Yonathan Prasetioso.
    NIM : 10.11.4517
    Kelas : S1 TI 1M

    1.) A matrix A is said to be antisymmetric if A : -At.

    a.) Example of antisymmetric matrix:
    A = 0 -4 8
    4 0 -7
    -8 7 0

    b.) Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements:
    A = 0 4 -2 B = 6 -4 8
    -4 0 8 -5 1 6
    3 -8 0 2 -4 0
    At = 0 -4 2 Bt = -6 4 -8
    4 0 -8 5 -1 -6
    -3 8 0 -2 4 0
    -At = 0 4 -2 -Bt = 6 -4 8
    -4 0 8 -5 1 6
    We could see that A != -At and B = -Bt. So it’s proved that antisymmetric matrix is a square matrix with zero on each diagonal elements.

    c.) Prove that sum of two antisymmetric matrix is an antisymmetric matrix.
    A = 0 4 9 B = 0 -3 8
    -4 0 5 3 0 -6
    -9 -5 0 -8 6 0
    (A+B) = 0 1 17
    -1 0 -1
    -17 1 0
    (A+B)t = 0 -1 -17 -(A+B)t = 0 1 17
    1 0 1 -1 0 -1
    17 -1 0 -17 1 0
    Can be seen that the results of (A+B) equal to -(A+B)t.
    Then it can be written (A+B) = – (A+B)t.

  28. NAMA : SURYAWAN PRIANTORO
    NIM : 10.11.4533
    KELAS: S1-TI 1M

    1.) Example of antisymmetric matrix:
    0 4 -2
    A = -3 2 5
    1 -5 0
    2.) Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements.
    Antisymmetric matrix is an anti of symmetric matrix, with (A= -At ). That mean the matrix is equal to its transpose, but each element of the transposed matrix has an opposite sign of the matrix.
    Here are two examples of symmetric matrix, one with zero on each diagonal elements.
    6 -2 1 6 5 9
    A = 4 2 5 B = -2 0 -1
    -8 -3 2 1 -4 2
    -6 2 1 -6 -5 -9
    At = -4 -2 -5 Bt = 2 0 1
    8 3 -2 -1 4 -2
    6 -2 1 6 5 9
    -At = 4 2 5 -Bt = -2 0 -1
    -8 -3 2 1 -4 2
    We could see that A != -At and B = -Bt. So it’s proved that antisymmetric matrix is a square matrix with zero on each diagonal elements.*
    3.) Prove that sum of two antisymmetric matrix is an antisymmetric matrix.
    1 2 1 4 -2 -5
    Let A = 3 0 3 , B = -1 0 4
    -2 3 0 5 -4 0
    1+4 2+(-2) 1+(-5)
    C = A + B = 3+(-1) 0+0 3+4
    -2+5 3+(-4) 0+0
    5 0 -4
    = 2 0 7
    3 -1 0
    5 0 -4
    Ct = 2 0 7
    3 -1 0
    -5 0 4
    -Ct = -2 0 -7
    -3 1 0
    C = -Ct (antisymmetric matrix)*

  29. 1. Example of antisymmetric matrix:
    5 4 2
    A = -1 3 0
    -1 3 -2
    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements.
    Antisymmetric matrix is an anti of symmetric matrix, with (A= -At ). That mean the matrix is equal to its transpose, but each element of the transposed matrix has an opposite sign of the matrix.
    Here are two examples of symmetric matrix, one with zero on each diagonal elements.
    3 1 0 -3 2 6
    A = -2 0 1 B = 2 -1 0
    1 2 1 3 -2 1

    -3 -1 0 3 -2 -6
    At = 2 0 -1 Bt = -2 1 0
    -1 -2 -1 -3 2 -1

    3 1 0 -3 2 6
    -At = -2 0 1 -Bt = 2 -1 0
    1 2 1 3 -2 1

    We could see that A != -At and B = -Bt. So it’s proved that antisymmetric matrix is a square matrix with zero on each diagonal elements.

    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.
    6 2 1 -3 2 0
    Let A = 1 -2 1 , B = 2 -2 1
    0 2 -1 3 2 0

    6+(-3) 2+2 1+0
    C = A + B = 1+2 -2+(-2) 1+1
    0+3 2+2 -1+0
    3 4 1
    = 3 0 2
    3 4 0

    -3 -4 -1
    Ct = -3 0 -2
    -3 -4 0

    3 4 1
    -Ct = 3 0 2
    3 4 0
    C = -Ct (antisymmetric matrix)

  30. Nama : Wahyu Adi Setyawan
    Kelas : S1 TI-M
    NIM : 10.11.4478

    1. Example of antisymmetric matrix:

    0 4 -2
    A = -3 2 5
    1 -5 0

    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements.

    Antisymmetric matrix is an anti of symmetric matrix, with (A= -At ). That mean the matrix is equal to its transpose, but each element of the transposed matrix has an opposite sign of the matrix.

    Here are two examples of symmetric matrix, one with zero on each diagonal elements.

    6 -2 1 6 5 9
    A = 4 2 5 B = -2 0 -1
    -8 -3 2 1 -4 2

    -6 2 1 -6 -5 -9
    At = -4 -2 -5 Bt = 2 0 1
    8 3 -2 -1 4 -2

    6 -2 1 6 5 9
    -At = 4 2 5 -Bt = -2 0 -1
    -8 -3 2 1 -4 2

    We could see that A != -At and B = -Bt. So it’s proved that antisymmetric matrix is a square matrix with zero on each diagonal elements.

    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.

    1 2 1 4 -2 -5
    Let A = 3 0 3 , B = -1 0 4
    -2 3 0 5 -4 0

    1+4 2+(-2) 1+(-5)
    C = A + B = 3+(-1) 0+0 3+4
    -2+5 3+(-4) 0+0

    5 0 -4
    = 2 0 7
    3 -1 0

    5 0 -4
    Ct = 2 0 7
    3 -1 0

    -5 0 4
    -Ct = -2 0 -7
    -3 1 0

    C = -Ct (antisymmetric matrix)

  31. Nama : Zakiul fahmi
    Nmor Mhsiswa : 10.11.4537
    Kelas : S1-TI-1M

    A)
    A= 0 -4 -6
    4 0 -1
    6 1 0

    B)
    A= 0 -2 5
    At = 0 2 -5
    -At = 0 -2 5
    2 0 -3 -2 0 3 2 0 -3
    -5 3 0 5 -3 2 -5 3 0

    ( 0 miring ke bawah sebagai diagonal Matrik )

    A = 1 -3 5
    Bt = 1 0 -4
    -Bt = -1 0 4
    0 6 -2 3 6 0 3 -6 0
    -4 0 8 5 -2 8 -5 2 -8

    ( kesimpulan : -At dan -Bt tidak sama
    -At mempunyai diagonal bernilai nol, maka terbukti bahwa arsymetrik -At mempunyai diagonal matriks )

    C)
    A = 0 -9 1
    b = 0 5 2 (a+b) = 0 -4 3
    9 0 -3 -5 0 1 4 0 -2
    -1 3 0 -2 -1 0 -3 2 0 ( sama )

    (A+B)t : 0 4 -3 -(A+B) : 0 4 3
    -4 0 2 4 0 -2
    3 -2 0 -3 2 0

    ( terbukti bahwa (A+B) = -(A+B)t (antysimatrik matriks) )

  32. Pembuktian dengan menggunakan Matlab 7.10

    1. Example of antisymmetric matrix:

    >> A=[0 -2 -1;-2 0 3;1 -3 0]

    A =

    0 -2 -1
    -2 0 3
    1 -3 0

    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements:

    >> A=[6 -3 8;3 1 7;-8 -7 4],B=[0 -3 8;3 0 7;-8 -7 0]

    A =

    6 -3 8
    3 1 7
    -8 -7 4

    B =

    0 -3 8
    3 0 7
    -8 -7 0

    >> A’,B’

    ans =

    6 3 -8
    -3 1 -7
    8 7 4

    ans =

    0 3 -8
    -3 0 -7
    8 7 0

    >> -A’,-B’

    ans =

    -6 -3 8
    3 -1 7
    -8 -7 -4

    ans =

    0 -3 8
    3 0 7
    -8 -7 0

    Kita bisa melihat bahwa A =-At dan B =-Bt. Jadi itu membuktikan bahwa antisimetrik matriks adalah matriks persegi dengan nol pada setiap elemen diagonal.

    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.

    >> A=[0 -4 8;4 0 -5;-8 5 0],B=[0 7 -3;-7 0 6;3 -6 0]

    A =

    0 -4 8
    4 0 -5
    -8 5 0

    B =

    0 7 -3
    -7 0 6
    3 -6 0

    >> C=A+B

    C =

    0 3 5
    -3 0 1
    -5 -1 0

    >> C’

    ans =

    0 -3 -5
    3 0 -1
    5 1 0

    >> -C’

    ans =

    0 3 5
    -3 0 1
    -5 -1 0

  33. NAMA : Yusiana Pambaruni
    NIM : 10.11.4497
    KELAS : S1 TI 1M

    1. Example of antisymmetric matrix:
    >> A=[0 -2 -1;-2 0 3;1 -3 0]
    A =
    0 -2 -1
    -2 0 3
    1 -3 0
    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements:
    >> A=[6 -3 8;3 1 7;-8 -7 4],B=[0 -3 8;3 0 7;-8 -7 0]
    A =
    6 -3 8
    3 1 7
    -8 -7 4
    B =
    0 -3 8
    3 0 7
    -8 -7 0
    >> A’,B’
    ans =
    6 3 -8
    -3 1 -7
    8 7 4
    ans =
    0 3 -8
    -3 0 -7
    8 7 0
    >> -A’,-B’
    ans =
    -6 -3 8
    3 -1 7
    -8 -7 -4
    ans =
    0 -3 8
    3 0 7
    -8 -7 0
    Kita bisa melihat bahwa A =-At dan B =-Bt. Jadi itu membuktikan bahwa antisimetrik matriks adalah matriks persegi dengan nol pada setiap elemen diagonal.
    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.
    >> A=[0 -4 8;4 0 -5;-8 5 0],B=[0 7 -3;-7 0 6;3 -6 0]
    A =
    0 -4 8
    4 0 -5
    -8 5 0
    B =
    0 7 -3
    -7 0 6
    3 -6 0
    >> C=A+B
    C =
    0 3 5
    -3 0 1
    -5 -1 0
    >> C’
    ans =
    0 -3 -5
    3 0 -1
    5 1 0
    >> -C’
    ans =
    0 3 5
    -3 0 1
    -5 -1 0
    C = -Ct (antisymmetric matrix berarti benar)

  34. NAMA : Gani Anggoro
    NIM : 10.11.4510
    KELAS : S1 TI 1M

    1. Example of antisymmetric matrix:
    >> A=[0 -2 -1;-2 0 3;1 -3 0]
    A =
    0 -2 -1
    -2 0 3
    1 -3 0
    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements:
    >> A=[6 -3 8;3 1 7;-8 -7 4],B=[0 -3 8;3 0 7;-8 -7 0]
    A =
    6 -3 8
    3 1 7
    -8 -7 4
    B =
    0 -3 8
    3 0 7
    -8 -7 0
    >> A’,B’
    ans =
    6 3 -8
    -3 1 -7
    8 7 4
    ans =
    0 3 -8
    -3 0 -7
    8 7 0
    >> -A’,-B’
    ans =
    -6 -3 8
    3 -1 7
    -8 -7 -4
    ans =
    0 -3 8
    3 0 7
    -8 -7 0
    Kita bisa melihat bahwa A =-At dan B =-Bt. Jadi itu membuktikan bahwa antisimetrik matriks adalah matriks persegi dengan nol pada setiap elemen diagonal.
    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.
    >> A=[0 -4 8;4 0 -5;-8 5 0],B=[0 7 -3;-7 0 6;3 -6 0]
    A =
    0 -4 8
    4 0 -5
    -8 5 0
    B =
    0 7 -3
    -7 0 6
    3 -6 0
    >> C=A+B
    C =
    0 3 5
    -3 0 1
    -5 -1 0
    >> C’
    ans =
    0 -3 -5
    3 0 -1
    5 1 0
    >> -C’
    ans =
    0 3 5
    -3 0 1
    -5 -1 0
    C = -Ct (antisymmetric matrix berarti benar)

  35. NAMA : AKHMAD NUR FAOSIN
    NIM : 10.11.4509
    KELAS : S1 TI 1M

    1. Example of antisymmetric matrix:
    >> A=[0 -2 -1;-2 0 3;1 -3 0]
    A =
    0 -2 -1
    -2 0 3
    1 -3 0
    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements:
    >> A=[6 -3 8;3 1 7;-8 -7 4],B=[0 -3 8;3 0 7;-8 -7 0]
    A =
    6 -3 8
    3 1 7
    -8 -7 4
    B =
    0 -3 8
    3 0 7
    -8 -7 0
    >> A’,B’
    ans =
    6 3 -8
    -3 1 -7
    8 7 4
    ans =
    0 3 -8
    -3 0 -7
    8 7 0
    >> -A’,-B’
    ans =
    -6 -3 8
    3 -1 7
    -8 -7 -4
    ans =
    0 -3 8
    3 0 7
    -8 -7 0
    Kita bisa melihat bahwa A =-At dan B =-Bt. Jadi itu membuktikan bahwa antisimetrik matriks adalah matriks persegi dengan nol pada setiap elemen diagonal.
    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.
    >> A=[0 -4 8;4 0 -5;-8 5 0],B=[0 7 -3;-7 0 6;3 -6 0]
    A =
    0 -4 8
    4 0 -5
    -8 5 0
    B =
    0 7 -3
    -7 0 6
    3 -6 0
    >> C=A+B
    C =
    0 3 5
    -3 0 1
    -5 -1 0
    >> C’
    ans =
    0 -3 -5
    3 0 -1
    5 1 0
    >> -C’
    ans =
    0 3 5
    -3 0 1
    -5 -1 0
    C = -Ct (antisymmetric matrix berarti benar)

  36. Nama : Helmy Ashari
    Nim : 10.11.4535
    Kls : S1 TI 1M

    a)
    A= 0 -4 -6
    4 0 -1
    6 1 0

    b)
    A= 0 -2 5
    At = 0 2 -5
    -At = 0 -2 5
    2 0 -3 -2 0 3 2 0 -3
    -5 3 0 5 -3 2 -5 3 0

    ( 0 miring ke bawah sebagai diagonal Matrik )

    A = 1 -3 5
    Bt = 1 0 -4
    -Bt = -1 0 4
    0 6 -2 3 6 0 3 -6 0
    -4 0 8 5 -2 8 -5 2 -8

    ( kesimpulan : -At dan -Bt tidak sama
    -At mempunyai diagonal bernilai nol, maka terbukti bahwa arsymetrik -At mempunyai diagonal matriks )

    c)
    A = 0 -9 1
    b = 0 5 2 (a+b) = 0 -4 3
    9 0 -3 -5 0 1 4 0 -2
    -1 3 0 -2 -1 0 -3 2 0 ( sama )

    (A+B)t : 0 4 -3 -(A+B) : 0 4 3
    -4 0 2 4 0 -2
    3 -2 0 -3 2 0

    ( terbukti bahwa (A+B) = -(A+B)t (antysimatrik matriks) )

  37. Nama : Nurul Qarama
    NIM : 10.11.4498
    Kelas : S1-TI 1M

    1. Example of antisymmetric matrix:

    0 4 -1
    A = -4 0 7
    1 -7 0

    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements.

    An antisymmetric matrix (skew-symmetric matrix) is a square matrix A whose transpose is also its negative; that is, it satisfies the equation A = −AT.

    Here are two examples of matrix, one with zero on each diagonal elements :

    6 -5 8 0 -5 8
    A = 3 1 9 B = 3 0 9
    -8 -9 6 -8 -9 0

    6 5 -8 0 -5 -8
    At = -3 1 -9 Bt = -3 0 -9
    8 9 6 8 9 0

    6 -5 8 0 -5 8
    -At = 3 1 9 -Bt = 3 0 9
    -8 -9 6 -8 -9 0

    We could see that A != -At and B = -Bt. So it’s proved that antisymmetric matrix is a square matrix with zero on each diagonal elements.

    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.

    0 -5 9 0 10 -6
    Let A = 5 0 -3 , B = -10 0 7
    -9 3 0 6 -7 0

    0+0 -5+10 9+(-6)
    C = A + B = 5+(-10) 0+0 -3+7
    -9+6 3+(-7) 0+0

    0 5 3
    = -5 0 4
    -3 -4 0

    0 -5 -3
    Ct = 5 0 -4
    3 4 0

    0 5 3
    -Ct = -5 0 4
    -3 -4 0

    C = -Ct (antisymmetric matrix)

  38. Nama : Nurul Qarama
    NIM : 10.11.4498
    Kelas : S1-TI 1M

    1. Example of antisymmetric matrix:

    0 4 -1
    A = -4 0 7
    1 -7 0

    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements.

    An antisymmetric matrix (skew-symmetric matrix) is a square matrix A whose transpose is also its negative; that is, it satisfies the equation A = −AT.

    Here are two examples of matrix, one with zero on each diagonal elements :

    6 -5 8 0 -5 8
    A = 3 1 9 B = 3 0 9
    -8 -9 6 -8 -9 0

    6 5 -8 0 -5 -8
    At = -3 1 -9 Bt = -3 0 -9
    8 9 6 8 9 0

    6 -5 8 0 -5 8
    -At = 3 1 9 -Bt = 3 0 9
    -8 -9 6 -8 -9 0

    We could see that A != -At and B = -Bt. So it’s proved that antisymmetric matrix is a square matrix with zero on each diagonal elements.

    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.

    0 -5 9 0 10 -6
    Let A = 5 0 -3 , B = -10 0 7
    -9 3 0 6 -7 0

    0+0 -5+10 9+(-6)
    C = A + B = 5+(-10) 0+0 -3+7
    -9+6 3+(-7) 0+0

    0 5 3
    = -5 0 4
    -3 -4 0

    0 -5 -3
    Ct = 5 0 -4
    3 4 0

    0 5 3
    -Ct = -5 0 4
    -3 -4 0

    C = -Ct (antisymmetric matrix)

  39. NIM : 10.11.4519
    Nama : Topan Aji Nugroho

    1. Example of antisymmetric matrix:
    5 4 2
    A = -1 3 0
    -1 3 -2
    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements.
    Antisymmetric matrix is an anti of symmetric matrix, with (A= -At ). That mean the matrix is equal to its transpose, but each element of the transposed matrix has an opposite sign of the matrix.
    Here are two examples of symmetric matrix, one with zero on each diagonal elements.
    3 1 0 -3 2 6
    A = -2 0 1 B = 2 -1 0
    1 2 1 3 -2 1

    -3 -1 0 3 -2 -6
    At = 2 0 -1 Bt = -2 1 0
    -1 -2 -1 -3 2 -1

    3 1 0 -3 2 6
    -At = -2 0 1 -Bt = 2 -1 0
    1 2 1 3 -2 1

    We could see that A != -At and B = -Bt. So it’s proved that antisymmetric matrix is a square matrix with zero on each diagonal elements.

    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.
    6 2 1 -3 2 0
    Let A = 1 -2 1 , B = 2 -2 1
    0 2 -1 3 2 0

    6+(-3) 2+2 1+0
    C = A + B = 1+2 -2+(-2) 1+1
    0+3 2+2 -1+0
    3 4 1
    = 3 0 2
    3 4 0

    -3 -4 -1
    Ct = -3 0 -2
    -3 -4 0

    3 4 1
    -Ct = 3 0 2
    3 4 0
    C = -Ct (antisymmetric matrix)

  40. NIM : 10.11.4519
    Nama : Topan Aji Nugroho

    1. Example of antisymmetric matrix:
    5 4 2
    A = -1 3 0
    -1 3 -2
    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements.
    Antisymmetric matrix is an anti of symmetric matrix, with (A= -At ). That mean the matrix is equal to its transpose, but each element of the transposed matrix has an opposite sign of the matrix.
    Here are two examples of symmetric matrix, one with zero on each diagonal elements.
    3 1 0 -3 2 6
    A = -2 0 1 B = 2 -1 0
    1 2 1 3 -2 1

    -3 -1 0 3 -2 -6
    At = 2 0 -1 Bt = -2 1 0
    -1 -2 -1 -3 2 -1

    3 1 0 -3 2 6
    -At = -2 0 1 -Bt = 2 -1 0
    1 2 1 3 -2 1

    We could see that A != -At and B = -Bt. So it’s proved that antisymmetric matrix is a square matrix with zero on each diagonal elements.

    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.
    6 2 1 -3 2 0
    Let A = 1 -2 1 , B = 2 -2 1
    0 2 -1 3 2 0

    6+(-3) 2+2 1+0
    C = A + B = 1+2 -2+(-2) 1+1
    0+3 2+2 -1+0
    3 4 1
    = 3 0 2
    3 4 0

    -3 -4 -1
    Ct = -3 0 -2
    -3 -4 0

    3 4 1
    -Ct = 3 0 2
    3 4 0
    C = -Ct (antisymmetric matrix)

  41. Nama : Nurul Qarama
    NIM : 10.11.4498
    kelas : S1-TI 1M

    1. Example of antisymmetric matrix:

    0 4 -1
    A = -4 0 7
    1 -7 0

    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements.

    An antisymmetric matrix (skew-symmetric matrix) is a square matrix A whose transpose is also its negative; that is, it satisfies the equation A = −AT.

    Here are two examples of matrix, one with zero on each diagonal elements :

    6 -5 8 0 -5 8
    A = 3 1 9 B = 3 0 9
    -8 -9 6 -8 -9 0

    6 5 -8 0 -5 -8
    At = -3 1 -9 Bt = -3 0 -9
    8 9 6 8 9 0

    6 -5 8 0 -5 8
    -At = 3 1 9 -Bt = 3 0 9
    -8 -9 6 -8 -9 0

    We could see that A != -At and B = -Bt. So it’s proved that antisymmetric matrix is a square matrix with zero on each diagonal elements.

    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.

    0 -5 9 0 10 -6
    Let A = 5 0 -3 , B = -10 0 7
    -9 3 0 6 -7 0

    0+0 -5+10 9+(-6)
    C = A + B = 5+(-10) 0+0 -3+7
    -9+6 3+(-7) 0+0

    0 5 3
    = -5 0 4
    -3 -4 0

    0 -5 -3
    Ct = 5 0 -4
    3 4 0

    0 5 3
    -Ct = -5 0 4
    -3 -4 0

    C = -Ct (antisymmetric matrix)

  42. NIM : 10.11.4483
    Nama : Tiyas Tri Kusumawati
    Kelas : S1 TI -M

    1. Example of antisymmetric matrix:
    2 -1 2
    A = 2 3 0
    1 -4 0
    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements.
    Antisymmetric matrix is an anti of symmetric matrix, with (A= -At ). That mean the matrix is equal to its transpose, but each element of the transposed matrix has an opposite sign of the matrix.
    Here are two examples of symmetric matrix, one with zero on each diagonal elements.
    2 4 0 2 -1 0
    A = -2 -1 0 B = 0 2 -5
    -2 -1 3 2 2 -1

    -2 -4 0 -2 1 0
    At = 2 1 0 Bt = 0 -2 5
    2 1 -3 -2 -2 1

    2 4 0 2 -1 0
    -At = -2 -1 0 -Bt = 0 -2 5
    -2 -1 3 2 2 -1

    We could see that A != -At and B = -Bt. So it’s proved that antisymmetric matrix is a square matrix with zero on each diagonal elements.

    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.
    2 -3 1 3 -4 2
    Let A = 1 -1 0 , B = 1 -2 3
    0 2 1 4 4 5

    2+3 -3+(-4) 1+2
    C = A + B = 1+1 -1+(-2) 0+3
    0+4 2+4 1+5
    5 -7 3
    = 2 -3 3
    4 6 6

    -5 7 -3
    Ct = -2 3 -3
    -4 -6 -6

    5 -7 3
    -Ct = 2 -3 3
    4 6 6
    C = -Ct (antisymmetric matrix)

  43. Nama : Ade Gunawan Mohamad Zainal Putra
    NIM : 10.11.4520
    Kelas : S1-TI 1M

    1. Example of antisymmetric matrix:

    0 3 -2
    A = -3 0 5
    2 -5 0

    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements.

    An antisymmetric matrix (skew-symmetric matrix) is a square matrix A whose transpose is also its negative; that is, it satisfies the equation A = −At.

    Here are two examples of matrix, one with zero on each diagonal elements :

    7 -4 9 0 -4 9
    A = 4 2 8 B = 4 0 8
    -9 -8 5 -9 -8 0

    7 4 -9 0 4 -9
    At = -4 2 -8 Bt = -4 0 -8
    9 8 5 9 8 0

    -7 -4 9 0 -4 9
    -At = 4 -2 8 -Bt = 4 0 8
    -9 -8 -5 -9 -8 0

    We could see that A != -At and B = -Bt. So it’s proved that antisymmetric matrix is a square matrix with zero on each diagonal elements.

    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.

    0 -3 7 0 11 -5
    Let A = 3 0 -4 , B = -11 0 8
    -7 4 0 5 -8 0

    0+0 -3+11 7+(-5)
    C = A + B = 3+(-11) 0+0 -4+8
    -7+5 4+(-8) 0+0

    0 8 2
    = -8 0 4
    -2 -4 0

    0 -8 -2
    Ct = 8 0 -4
    2 4 0

    0 8 2
    -Ct = -8 0 4
    -2 -4 0

    C = -Ct (antisymmetric matrix) Proved!

  44. NIM : 10.11.4518
    Nama : Sinta Sulistyaningsih

    1. Example of antisymmetric matrix:
    1 1 0
    A = -3 2 1
    1 -4 0
    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements.
    Antisymmetric matrix is an anti of symmetric matrix, with (A= -At ). That mean the matrix is equal to its transpose, but each element of the transposed matrix has an opposite sign of the matrix.
    Here are two examples of symmetric matrix, one with zero on each diagonal elements.
    1 2 1 2 1 -2
    A = -1 0 2 B = -1 -3 0
    -2 -1 3 2 -1 3

    -1 -2 -1 -2 -1 2
    At = -1 0 -2 Bt = 1 3 0
    2 1 -3 -2 1 -3

    1 2 1 2 1 -2
    -At = -1 0 2 -Bt = -1 -3 0
    -2 -1 3 2 -1 3

    We could see that A != -At and B = -Bt. So it’s proved that antisymmetric matrix is a square matrix with zero on each diagonal elements.

    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.
    1 2 -2 0 -1 3
    Let A = 3 1 -2 , B = 2 -2 1
    3 1 1 4 2 1

    1+0 2+(-1) -2+3
    C = A + B = 3+2 1+(-2) -2+1
    3+4 1+2 1+1
    1 1 1
    = 5 -1 -1
    7 3 2

    -1 -1 -1
    Ct = -5 1 1
    -7 -3 -2

    1 1 1
    -Ct = 5 -1 -1
    7 3 2
    C = -Ct (antisymmetric matrix)

  45. NIM : 10.11.4482
    Nama : Listiyaningsih
    Kelas : S1 TI M

    1. Example of antisymmetric matrix:
    1 3 -3
    A = -3 2 2
    1 -4 0
    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements.
    Antisymmetric matrix is an anti of symmetric matrix, with (A= -At ). That mean the matrix is equal to its transpose, but each element of the transposed matrix has an opposite sign of the matrix.
    Here are two examples of symmetric matrix, one with zero on each diagonal elements.
    3 -1 0 3 3 2
    A = 2 2 1 B = -2 0 4
    -2 -1 3 1 1 -3

    -3 1 0 -3 -3 -2
    At = -2 -2 -1 Bt = 2 0 -4
    2 1 -3 -1 -1 3

    3 -1 0 3 3 2
    -At = 2 2 1 -Bt = -2 0 4
    -2 -1 3 1 1 -3

    We could see that A != -At and B = -Bt. So it’s proved that antisymmetric matrix is a square matrix with zero on each diagonal elements.

    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.
    2 1 -3 2 2 -4
    Let A = 0 1 -2 , B = 1 -3 1
    3 -1 3 4 2 1

    2+2 1+2 -3+(-4)
    C = A + B = 0+1 1+(-3) -2+1
    3+4 -1+2 3+1
    4 3 -7
    = 1 -5 -1
    7 1 4

    -4 -3 7
    Ct = -1 5 1
    -7 -1 -4

    4 3 -7
    -Ct = 1 -5 -1
    7 1 4
    C = -Ct (antisymmetric matrix)

  46. Nama : Lisman prihadi
    Nim : 10.11.4493
    Kls : S1 TI 1M

    a) A= 0 -4 -6
    4 0 -1
    6 1 0

    b) A= 0 -2 5 At = 0 2 -5 -At = 0 -2 5
    2 0 -3 -2 0 3 2 0 -3
    -5 3 0 5 -3 2 -5 3 0

    0 miring ke bawah sebagai diagonal Matrik

    A = 1 -3 5 Bt = 1 0 -4 -Bt = -1 0 4
    0 6 -2 3 6 0 3 -6 0
    -4 0 8 5 -2 8 -5 2 -8

    kesimpulan : -At dan -Bt tidak sama
    -At mempunyai diagonal bernilai nol, maka terbukti bahwa arsymetrik -At mempunyai diagonal matriks

    c) A = 0 -9 1 b = 0 5 2 (a+b) = 0 -4 3
    9 0 -3 -5 0 1 4 0 -2
    -1 3 0 -2 -1 0 -3 2 0 sama

    (A+B)t : 0 4 -3 -(A+B) : 0 4 3
    -4 0 2 4 0 -2
    3 -2 0 -3 2 0

    terbukti bahwa (A+B) = -(A+B)t (antysimatrik matriks)

  47. Nim : 4491

    1. Example of antisymmetric matrix:
    >> A=[0 -2 -1;-2 0 3;1 -3 0]
    A =
    0 -2 -1
    -2 0 3
    1 -3 0

    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements:
    >> A=[6 -3 8;3 1 7;-8 -7 4],B=[0 -3 8;3 0 7;-8 -7 0]
    A =
    6 -3 8
    3 1 7
    -8 -7 4
    B =
    0 -3 8
    3 0 7
    -8 -7 0
    >> A’,B’
    ans =
    6 3 -8
    -3 1 -7
    8 7 4
    ans =
    0 3 -8
    -3 0 -7
    8 7 0
    >> -A’,-B’
    ans =
    -6 -3 8
    3 -1 7
    -8 -7 -4
    ans =
    0 -3 8
    3 0 7
    -8 -7 0

    We could see that A != -At and B = -Bt. So it’s proved that antisymmetric matrix is a square matrix with zero on each diagonal elements.

    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.
    >> A=[0 -4 8;4 0 -5;-8 5 0],B=[0 7 -3;-7 0 6;3 -6 0]
    A =
    0 -4 8
    4 0 -5
    -8 5 0
    B =
    0 7 -3
    -7 0 6
    3 -6 0
    >> C=A+B
    C =
    0 3 5
    -3 0 1
    -5 -1 0
    >> C’
    ans =
    0 -3 -5
    3 0 -1
    5 1 0
    >> -C’
    ans =
    0 3 5
    -3 0 1
    -5 -1 0
    C = -Ct (antisymmetric matrix)

  48. Nim : 4491

    1. Example of antisymmetric matrix:
    >> A=[0 -2 -1;-2 0 3;1 -3 0]
    A =
    0 -2 -1
    -2 0 3
    1 -3 0

    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements:
    >> A=[6 -3 8;3 1 7;-8 -7 4],B=[0 -3 8;3 0 7;-8 -7 0]
    A =
    6 -3 8
    3 1 7
    -8 -7 4
    B =
    0 -3 8
    3 0 7
    -8 -7 0
    >> A’,B’
    ans =
    6 3 -8
    -3 1 -7
    8 7 4
    ans =
    0 3 -8
    -3 0 -7
    8 7 0
    >> -A’,-B’
    ans =
    -6 -3 8
    3 -1 7
    -8 -7 -4
    ans =
    0 -3 8
    3 0 7
    -8 -7 0

    We could see that A != -At and B = -Bt. So it’s proved that antisymmetric matrix is a square matrix with zero on each diagonal elements.

    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.
    >> A=[0 -4 8;4 0 -5;-8 5 0],B=[0 7 -3;-7 0 6;3 -6 0]
    A =
    0 -4 8
    4 0 -5
    -8 5 0
    B =
    0 7 -3
    -7 0 6
    3 -6 0
    >> C=A+B
    C =
    0 3 5
    -3 0 1
    -5 -1 0
    >> C’
    ans =
    0 -3 -5
    3 0 -1
    5 1 0
    >> -C’
    ans =
    0 3 5
    -3 0 1
    -5 -1 0
    C = -Ct (antisymmetric matrix)

  49. Nama : Lisman Prihadi
    NIM : 10.11.4493
    Kelas : S1 TI M

    1. Example of antisymmetric matrix:

    0 4 -2
    A = -3 2 5
    1 -5 0

    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements.

    Antisymmetric matrix is an anti of symmetric matrix, with (A= -At ). That mean the matrix is equal to its transpose, but each element of the transposed matrix has an opposite sign of the matrix.

    Here are two examples of symmetric matrix, one with zero on each diagonal elements.

    6 -2 1 6 5 9
    A = 4 2 5 B = -2 0 -1
    -8 -3 2 1 -4 2

    -6 2 1 -6 -5 -9
    At = -4 -2 -5 Bt = 2 0 1
    8 3 -2 -1 4 -2

    6 -2 1 6 5 9
    -At = 4 2 5 -Bt = -2 0 -1
    -8 -3 2 1 -4 2

    We could see that A != -At and B = -Bt. So it’s proved that antisymmetric matrix is a square matrix with zero on each diagonal elements.

    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.

    1 2 1 4 -2 -5
    Let A = 3 0 3 , B = -1 0 4
    -2 3 0 5 -4 0

    1+4 2+(-2) 1+(-5)
    C = A + B = 3+(-1) 0+0 3+4
    -2+5 3+(-4) 0+0

    5 0 -4
    = 2 0 7
    3 -1 0

    5 0 -4
    Ct = 2 0 7
    3 -1 0

    -5 0 4
    -Ct = -2 0 -7
    -3 1 0

    C = -Ct (antisymmetric matrix)

  50. NAMA : FENDI PRIYANTO
    NIM : 10.11.4488
    KELAS : SI TI / M

    Dengan menggunakan matlab 7.10
    1. Example of antisymmetric matrix:
    >> A=[0 -2 -1;-2 0 3;1 -3 0]
    A =
    0 -2 -1
    -2 0 3
    1 -3 0
    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements:
    >> A=[6 -3 8;3 1 7;-8 -7 4],B=[0 -3 8;3 0 7;-8 -7 0]
    A =
    6 -3 8
    3 1 7
    -8 -7 4
    B =
    0 -3 8
    3 0 7
    -8 -7 0
    >> A’,B’
    ans =
    6 3 -8
    -3 1 -7
    8 7 4
    ans =
    0 3 -8
    -3 0 -7
    8 7 0
    >> -A’,-B’
    ans =
    -6 -3 8
    3 -1 7
    -8 -7 -4
    ans =
    0 -3 8
    3 0 7
    -8 -7 0
    Kita bisa melihat bahwa A =-At dan B =-Bt. Jadi itu membuktikan bahwa antisimetrik matriks adalah matriks persegi dengan nol pada setiap elemen diagonal.
    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.
    >> A=[0 -4 8;4 0 -5;-8 5 0],B=[0 7 -3;-7 0 6;3 -6 0]
    A =
    0 -4 8
    4 0 -5
    -8 5 0
    B =
    0 7 -3
    -7 0 6
    3 -6 0
    >> C=A+B
    C =
    0 3 5
    -3 0 1
    -5 -1 0
    >> C’
    ans =
    0 -3 -5
    3 0 -1
    5 1 0
    >> -C’
    ans =
    0 3 5
    -3 0 1
    -5 -1 0
    C = -Ct antisymmetric matrix berarti benar

  51. Nama : Doni Rusman Teja
    NIM : 10.11.4492
    Kelas : S1 TI M

    1. Example of antisymmetric matrix:

    0 4 -2
    A = -3 2 5
    1 -5 0

    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements.

    Antisymmetric matrix is an anti of symmetric matrix, with (A= -At ). That mean the matrix is equal to its transpose, but each element of the transposed matrix has an opposite sign of the matrix.

    Here are two examples of symmetric matrix, one with zero on each diagonal elements.

    6 -2 1 6 5 9
    A = 4 2 5 B = -2 0 -1
    -8 -3 2 1 -4 2

    -6 2 1 -6 -5 -9
    At = -4 -2 -5 Bt = 2 0 1
    8 3 -2 -1 4 -2

    6 -2 1 6 5 9
    -At = 4 2 5 -Bt = -2 0 -1
    -8 -3 2 1 -4 2

    We could see that A != -At and B = -Bt. So it’s proved that antisymmetric matrix is a square matrix with zero on each diagonal elements.

    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.

    1 2 1 4 -2 -5
    Let A = 3 0 3 , B = -1 0 4
    -2 3 0 5 -4 0

    1+4 2+(-2) 1+(-5)
    C = A + B = 3+(-1) 0+0 3+4
    -2+5 3+(-4) 0+0

    5 0 -4
    = 2 0 7
    3 -1 0

    5 0 -4
    Ct = 2 0 7
    3 -1 0

    -5 0 4
    -Ct = -2 0 -7
    -3 1 0

    C = -Ct (antisymmetric matrix)

  52. 1. Example of antisymmetric matrix:

    0 4 -3
    A = -4 0 6
    3 -6 0

    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements.

    Antisymmetric matrix is an anti of symmetric matrix, with (A= -At ). That mean the matrix is equal to its transpose, but each element of the transposed matrix has an opposite sign of the matrix.

    Here are two examples of symmetric matrix, one with zero on each diagonal elements.

    7 -5 7 0 -5 7
    A = 5 2 8 B = 5 0 8
    -7 -8 5 -7 -8 0

    7 5 -7 0 5 -7
    At = -5 2 -8 Bt = -5 0 -8
    7 8 5 7 8 0

    -7 -5 7 0 -5 7
    -At = 5 -2 8 -Bt = 5 0 8
    -7 -8 -5 -7 -8 0

    We could see that A != -At and B = -Bt. So it’s proved that antisymmetric matrix is a square matrix with zero on each diagonal elements.

    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.

    0 -2 4 0 7 -5
    Let A = 2 0 -6 , B = -7 0 3
    -4 6 0 5 -3 0

    C = A + B
    A B C
    0 -2 4 0 7 -5 0 5 -1
    2 0 -6 + -7 0 3 = -5 0 -3
    -4 6 0 5 -3 0 1 3 0

    Ct = 0 -5 -1
    5 0 3
    -1 -3 0

    -Ct = 0 5 -1
    -5 0 -3
    1 3 0
    C = -Ct (antisymmetric matrix)
    So A+B dapat dituliskan -(A+B)t

  53. Nama : Dyta Romania
    Kelas : 1M
    NIM : 10.11.4500

    1. Example of antisymmetric matrix:

    0 4 -3
    A = -4 0 6
    3 -6 0

    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements.

    Antisymmetric matrix is an anti of symmetric matrix, with (A= -At ). That mean the matrix is equal to its transpose, but each element of the transposed matrix has an opposite sign of the matrix.

    Here are two examples of symmetric matrix, one with zero on each diagonal elements.

    7 -5 7 0 -5 7
    A = 5 2 8 B = 5 0 8
    -7 -8 5 -7 -8 0

    7 5 -7 0 5 -7
    At = -5 2 -8 Bt = -5 0 -8
    7 8 5 7 8 0

    -7 -5 7 0 -5 7
    -At = 5 -2 8 -Bt = 5 0 8
    -7 -8 -5 -7 -8 0

    We could see that A != -At and B = -Bt. So it’s proved that antisymmetric matrix is a square matrix with zero on each diagonal elements.

    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.

    0 -2 4 0 7 -5
    Let A = 2 0 -6 , B = -7 0 3
    -4 6 0 5 -3 0

    C = A + B
    A B C
    0 -2 4 0 7 -5 0 5 -1
    2 0 -6 + -7 0 3 = -5 0 -3
    -4 6 0 5 -3 0 1 3 0

    Ct = 0 -5 -1
    5 0 3
    -1 -3 0

    -Ct = 0 5 -1
    -5 0 -3
    1 3 0
    C = -Ct (antisymmetric matrix)
    So A+B dapat dituliskan -(A+B)t

  54. Nama : Lisman Prihadi
    NIM : 10.11.4493
    Kelas : S1 TI M

    1. Example of antisymmetric matrix:

    0 4 -2
    A = -3 2 5
    1 -5 0

    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements.

    Antisymmetric matrix is an anti of symmetric matrix, with (A= -At ). That mean the matrix is equal to its transpose, but each element of the transposed matrix has an opposite sign of the matrix.

    Here are two examples of symmetric matrix, one with zero on each diagonal elements.

    6 -2 1 6 5 9
    A = 4 2 5 B = -2 0 -1
    -8 -3 2 1 -4 2

    -6 2 1 -6 -5 -9
    At = -4 -2 -5 Bt = 2 0 1
    8 3 -2 -1 4 -2

    6 -2 1 6 5 9
    -At = 4 2 5 -Bt = -2 0 -1
    -8 -3 2 1 -4 2

    We could see that A != -At and B = -Bt. So it’s proved that antisymmetric matrix is a square matrix with zero on each diagonal elements.

    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.

    1 2 1 4 -2 -5
    Let A = 3 0 3 , B = -1 0 4
    -2 3 0 5 -4 0

    1+4 2+(-2) 1+(-5)
    C = A + B = 3+(-1) 0+0 3+4
    -2+5 3+(-4) 0+0

    5 0 -4
    = 2 0 7
    3 -1 0

    5 0 -4
    Ct = 2 0 7
    3 -1 0

    -5 0 4
    -Ct = -2 0 -7
    -3 1 0

    C = -Ct (antisymmetric matrix)

  55. Nama : Lisman Prihadi
    NIM : 10.11.4493
    Kelas : S1 TI M

    1. Example of antisymmetric matrix:

    0 4 -2
    A = -3 2 5
    1 -5 0

    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements.

    Antisymmetric matrix is an anti of symmetric matrix, with (A= -At ). That mean the matrix is equal to its transpose, but each element of the transposed matrix has an opposite sign of the matrix.

    Here are two examples of symmetric matrix, one with zero on each diagonal elements.

    6 -2 1 6 5 9
    A = 4 2 5 B = -2 0 -1
    -8 -3 2 1 -4 2

    -6 2 1 -6 -5 -9
    At = -4 -2 -5 Bt = 2 0 1
    8 3 -2 -1 4 -2

    6 -2 1 6 5 9
    -At = 4 2 5 -Bt = -2 0 -1
    -8 -3 2 1 -4 2

    We could see that A != -At and B = -Bt. So it’s proved that antisymmetric matrix is a square matrix with zero on each diagonal elements.

    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.

    1 2 1 4 -2 -5
    Let A = 3 0 3 , B = -1 0 4
    -2 3 0 5 -4 0

    1+4 2+(-2) 1+(-5)
    C = A + B = 3+(-1) 0+0 3+4
    -2+5 3+(-4) 0+0

    5 0 -4
    = 2 0 7
    3 -1 0

    5 0 -4
    Ct = 2 0 7
    3 -1 0

    -5 0 4
    -Ct = -2 0 -7
    -3 1 0

    C = -Ct (antisymmetric matrix)

  56. Nama : MUHAMMAD YUSUF
    Kelas : S1 TI-1M
    NIM : 10.11.4469

    1. Example of antisymmetric matrix:
    0 4 -2
    A = -3 2 5
    1 -5 0

    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements.
    Antisymmetric matrix is an anti of symmetric matrix, with (A= -At ). That mean the matrix is equal to its transpose, but each element of the transposed matrix has an opposite sign of the matrix.
    Here are two examples of symmetric matrix, one with zero on each diagonal elements.
    6 -2 1 6 5 9
    A = 4 2 5 B = -2 0 -1
    -8 -3 2 1 -4 2
    -6 2 1 -6 -5 -9
    At = -4 -2 -5 Bt = 2 0 1
    8 3 -2 -1 4 -2
    6 -2 1 6 5 9
    -At = 4 2 5 -Bt = -2 0 -1
    -8 -3 2 1 -4 2
    We could see that A != -At and B = -Bt. So it’s proved that antisymmetric matrix is a square matrix with zero on each diagonal elements.

    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.
    1 2 1 4 -2 -5
    Let A = 3 0 3 , B = -1 0 4
    -2 3 0 5 -4 0
    1+4 2+(-2) 1+(-5)
    C = A + B = 3+(-1) 0+0 3+4
    -2+5 3+(-4) 0+0
    5 0 -4
    = 2 0 7
    3 -1 0
    5 0 -4
    Ct = 2 0 7
    3 -1 0
    -5 0 4
    -Ct = -2 0 -7
    -3 1 0
    C = -Ct (antisymmetric matrix)

  57. 1. Example of antisymmetric matrix:
    A=[1 2 1;2 0 3; 2 2 0]

    A =

    1 2 1
    2 0 3
    2 2 0

    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements:
    >> A=[0 1 1;2 3 1; 2 1 2],B=[2 1 1; 2 3 1;2 1 0]

    A =

    0 1 1
    2 3 1
    2 1 2

    B =

    2 1 1
    2 3 1
    2 1 0

    >> A’,B’

    ans =

    0 2 2
    1 3 1
    1 1 2

    ans =

    2 2 2
    1 3 1
    1 1 0
    Kita bisa melihat bahwa A =-At dan B =-Bt. Jadi itu membuktikan bahwa antisimetrik matriks adalah matriks persegi dengan nol pada setiap elemen diagonal.

    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.
    >> A=[1 2 4; 0 2 1;1 2 4],B=[1 2 3;1 0 1;2 3 1]

    A =

    1 2 4
    0 2 1
    1 2 4

    B =

    1 2 3
    1 0 1
    2 3 1

    >> C=A+B

    C =

    2 4 7
    1 2 2
    3 5 5

    >> C’

    ans =

    2 1 3
    4 2 5
    7 2 5

    >> -C’

    ans =

    -2 -1 -3
    -4 -2 -5
    -7 -2 -5
    Hasil dari (A+B) samadengan -(A+B)t.
    Maka dapat dituliskan (A+B) = – (A+B)t.

  58. Nama : Hampron Triandoko
    NIM : 10.11.4529
    Kelas : S1 TI 1M

    1. Example of antisymmetric matrix:

    0 4 -2
    A = -3 2 5
    1 -5 0

    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements.

    Antisymmetric matrix is an anti of symmetric matrix, with (A= -At ). That mean the matrix is equal to its transpose, but each element of the transposed matrix has an opposite sign of the matrix.

    Here are two examples of symmetric matrix, one with zero on each diagonal elements.

    6 -2 1 6 5 9
    A = 4 2 5 B = -2 0 -1
    -8 -3 2 1 -4 2

    -6 2 1 -6 -5 -9
    At = -4 -2 -5 Bt = 2 0 1
    8 3 -2 -1 4 -2

    6 -2 1 6 5 9
    -At = 4 2 5 -Bt = -2 0 -1
    -8 -3 2 1 -4 2

    We could see that A != -At and B = -Bt. So it’s proved that antisymmetric matrix is a square matrix with zero on each diagonal elements.

    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.

    1 2 1 4 -2 -5
    Let A = 3 0 3 , B = -1 0 4
    -2 3 0 5 -4 0

    1+4 2+(-2) 1+(-5)
    C = A + B = 3+(-1) 0+0 3+4
    -2+5 3+(-4) 0+0

    5 0 -4
    = 2 0 7
    3 -1 0

    5 0 -4
    Ct = 2 0 7
    3 -1 0

    -5 0 4
    -Ct = -2 0 -7
    -3 1 0

    C = -Ct (antisymmetric matrix)

  59. 1. Example of antisymmetric matrix:
    A=[1 2 3;4 0 3;1 2 0]

    A =

    1 2 3
    4 0 3
    1 2 0

    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements:
    >> A=[0 2 3;1 2 1;3 2 1],B=[2 0 1;2 1 1; 0 3 2]

    A =

    0 2 3
    1 2 1
    3 2 1

    B =

    2 0 1
    2 1 1
    0 3 2

    >> A’,B’

    ans =

    0 1 3
    2 2 2
    3 1 1

    ans =

    2 2 0
    0 1 3
    1 1 2

    >> -A’,-B’

    ans =

    0 -1 -3
    -2 -2 -2
    -3 -1 -1

    ans =

    -2 -2 0
    0 -1 -3
    -1 -1 -2
    A =-At dan B =-Bt. Jadi membuktikan bahwa antisimetrik matriks adalah matriks persegi dengan nol pada setiap elemen diagonal.

    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.
    >> A=[1 2 3;4 3 1;0 2 1],B=[1 2 3;0 3 2;1 4 1]

    A =

    1 2 3
    4 3 1
    0 2 1

    B =

    1 2 3
    0 3 2
    1 4 1

    >> C=A+B

    C =

    2 4 6
    4 6 3
    1 6 2

    >> C’

    ans =

    2 4 1
    4 6 6
    6 3 2

    >> -C’

    ans =

    -2 -4 -1
    -4 -6 -6
    -6 -3 -2
    Hasil dari (A+B) samadengan -(A+B)t.
    Maka dapat dituliskan (A+B) = – (A+B)t.

  60. Nama : Dyta Romania
    NIM : 10.11.4500
    kelas : 1M

    1.Example of antisymmetric matrix:

    A = 0 5 -2
    -3 0 -5
    2 3 0
    2.Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements.

    Antisymmetric matrix is an anti of symmetric matrix, with (A= -At ). That mean the matrix is equal to its transpose, but each element of the transposed matrix has an opposite sign of the matrix.

    Here are two examples of symmetric matrix, one with zero on each diagonal elements.

    A = 1 3 5 B = 0 3 5
    -3 2 7 -3 0 7
    -5 -7 4 -5 -7 0

    At = 1 -3 -5 Bt = 0 -3 -5
    3 2 -7 3 0 -7
    5 7 4 5 7 0

    -At = -1 3 5 -Bt = 0 3 5
    3 -2 7 -3 0 7
    -5 -7 -4 -5 -7 0

    We could see that A != -At and B = -Bt. So it’s proved that antisymmetric matrix is a square matrix with zero on each diagonal elements.
    3.Prove that sum of two antisymmetric matrix is an antisymmetric matrix.

    Let A = 0 2 -5 Let B = 0 -3 -5
    -2 0 -3 3 0 9
    5 3 0 5 -9 0

    C = A+B

    A B C
    0 2 -5 0 -3 -5 0 -1 -10
    -2 0 -3 + 3 0 9 = 1 0 6
    5 3 0 5 -9 0 10 -6 0

    Ct = 0 1 10
    -1 0 -6
    -10 6 0

    -Ct = 0 -1 -10
    1 0 6
    10 -6 0

    So C= -Ct merupakan antisymmetric matrix…. terbukti….///>

  61. Nama : Rakhmat Solihin
    NIM : 10.11.4507
    Kelas : S1.TI.1M
    1. Example of antisymmetric matrix:
    0 3 -2
    A = -3 0 1
    2 -1 0
    2. Prove that antisymmetric matrix is a square matrix with
    zero on each diagonal elements.
    Antisymmetric matrix is an anti of symmetric matrix, with (A= -At ). That mean the matrix is equal to its transpose, but each element of the transposed matrix has an opposite sign of the matrix.
    Here are two examples of symmetric matrix, one with zero on each diagonal elements.
    8 -4 9 0 -4 9
    A = 4 5 6 B = 4 0 6
    -9 -6 3 -9 -6 0
    8 4 -9 0 4 -9
    At = -4 5 -6 Bt = -4 0 -6
    9 6 3 9 6 0
    -8 -4 9 0 -4 9
    -At = 4 -5 6 -Bt = 4 0 6
    -9 -6 -3 -9 -6 0
    We could see that A != -At and B = -Bt. So it’s proved that antisymmetric matrix is a square matrix with zero on each diagonal elements.
    3. Prove that sum of two antisymmetric matrix is an
    antisymmetric matrix.
    0 -4 9 0 3 -8
    A = 4 0 -6 , B = -3 0 7
    -9 6 0 8 -7 0
    0+0 -4+3 9+(-8)
    C = A + B = 4+(-3) 0+0 -6+7
    -9+8 6+(-7) 0+0
    0 -1 1
    = 1 0 1
    -1 -1 0
    0 1 -1
    Ct = -1 0 -1
    1 1 0
    0 -1 1
    -Ct = 1 0 1
    -1 -1 0
    C = -Ct (antisymmetric matrix)

  62. Nama

    1.Example of antisymmetric matrix:

    A = 0 5 -2
    -3 0 -5
    2 3 0

    2.Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements.

    Antisymmetric matrix is an anti of symmetric matrix, with (A= -At ). That mean the matrix is equal to its transpose, but each element of the transposed matrix has an opposite sign of the matrix.

    Here are two examples of symmetric matrix, one with zero on each diagonal elements.
    A = 1 3 5 B = 0 3 5
    -3 2 7 -3 0 7
    -5 -7 4 -5 -7 0

    At = 1 -3 -5 Bt = 0 -3 -5
    3 2 -7 3 0 -7
    5 7 4 5 7 0

    -At = -1 3 5 -Bt = 0 3 5
    -3 -2 7 -3 0 7
    -5 -7 -4 -5 -7 0

    We could see that A != -At and B = -Bt. So it’s proved that antisymmetric matrix is a square matrix with zero on each diagonal elements.
    3.Prove that sum of two antisymmetric matrix is an antisymmetric matrix.

    Let A = 0 2 -5 Let B = 0 -3 -5
    -2 0 -3 3 0 9
    5 3 0 5 -9 0

    C = A+B
    A B C
    0 2 -5 0 -3 -5 0 -1 -10
    -2 0 -3 + 3 0 9 = 1 0 6
    5 3 0 5 -9 0 10 -6 0

    Ct = 0 1 10
    -1 0 -6
    -10 6 0

    -Ct = 0 -1 -10
    1 0 6
    10 -6 0

    So C = – Ct antisyimmetric matric True…

  63. NIM: 10.11.4475

    1. Example of antisymmetric matrix:
    >> A=[0 -2 -1;-2 0 3;1 -3 0]
    A =
    0 -2 -1
    -2 0 3
    1 -3 0
    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements:
    >> A=[6 -3 8;3 1 7;-8 -7 4],B=[0 -3 8;3 0 7;-8 -7 0]
    A =
    6 -3 8
    3 1 7
    -8 -7 4
    B =
    0 -3 8
    3 0 7
    -8 -7 0
    >> A’,B’
    ans =
    6 3 -8
    -3 1 -7
    8 7 4
    ans =
    0 3 -8
    -3 0 -7
    8 7 0
    >> -A’,-B’
    ans =
    -6 -3 8
    3 -1 7
    -8 -7 -4
    ans =
    0 -3 8
    3 0 7
    -8 -7 0
    Kita bisa melihat bahwa A =-At dan B =-Bt. Jadi itu membuktikan bahwa antisimetrik matriks adalah matriks persegi dengan nol pada setiap elemen diagonal.
    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.
    >> A=[0 -4 8;4 0 -5;-8 5 0],B=[0 7 -3;-7 0 6;3 -6 0]
    A =
    0 -4 8
    4 0 -5
    -8 5 0
    B =
    0 7 -3
    -7 0 6
    3 -6 0
    >> C=A+B
    C =
    0 3 5
    -3 0 1
    -5 -1 0
    >> C’
    ans =
    0 -3 -5
    3 0 -1
    5 1 0
    >> -C’
    ans =
    0 3 5
    -3 0 1
    -5 -1 0
    C = -Ct (antisymmetric matrix berarti benar)

  64. Nama : Dian Nur A.
    NIM : 10.11.4516
    Kelas : S1 TI 1M

    1. Example of antisymmetric matrix:
    A = 0 -5 9
    5 0 -7
    -9 7 0

    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements:
    A = 0 2 -1
    -2 0 7
    1 -7 0

    At = 0 -2 1
    2 0 -7
    -1 7 0

    -At = 0 2 -1
    -2 0 7
    1 -7 0

    B = 4 -2 7
    -3 1 5
    6 -8 0

    Bt = 4 -3 6
    -2 1 -8
    7 5 0

    -Bt = -4 3 -6
    2 -1 8
    -7 -5 0

    dari pembuktian di atas, -At dan -Bt berbeda. Terbukti bahwa -At mempunyai diagonal nol. Maka antisymetric -At mempunyai diagonal matrik.

    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.
    A = 0 4 9
    -4 0 5
    -9 -5 0

    B = 0 -3 8
    3 0 -6
    -8 6 0

    (A+B) = 0 1 17
    -1 0 -1
    -17 1 0

    (A+B)t = 0 -1 -17
    1 0 1
    17 -1 0

    -(A+B)t = 0 1 17
    -1 0 -1
    -17 1 0

    Dapat dilihat bahwa hasil dari (A+B) sama dengan -(A+B)t.
    Maka dapat dituliskan (A+B) = – (A+B)t.

  65. Nama : Dian Nur A.
    NIM : 10.11.4516
    Kelas : S1 TI 1M

    1. Example of antisymmetric matrix:
    A = 0 -5 9
    5 0 -7
    -9 7 0

    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements:
    A = 0 2 -1 B = 4 -2 7
    -2 0 7 -3 1 5
    1 -7 0 6 -8 0

    At = 0 -2 1 Bt = 4 -3 6
    2 0 -7 -2 1 -8
    -1 7 0 7 5 0

    -At = 0 2 -1 -Bt = -4 3 -6
    -2 0 7 2 -1 8
    1 -7 0 -7 -5 0

    dari pembuktian di atas, -At dan -Bt berbeda. Terbukti bahwa -At mempunyai diagonal nol. Maka antisymetric -At mempunyai diagonal matrik.

    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.
    A = 0 4 9 B = 0 -3 8
    -4 0 5 3 0 -6
    -9 -5 0 -8 6 0

    (A+B) = 0 1 17
    -1 0 -1
    -17 1 0

    (A+B)t = 0 -1 -17 -(A+B)t = 0 1 17
    1 0 1 -1 0 -1
    17 -1 0 -17 1 0

    Dapat dilihat bahwa hasil dari (A+B) sama dengan -(A+B)t.
    Maka dapat dituliskan (A+B) = – (A+B)t.

  66. Nama : Septian Dwi Cahyono
    Kelas : S1 TI 1M
    NIM : 10.11.4512

    1. Example of antisymmetric matrix:
    >> A=[0 -2 -1;-2 0 3;1 -3 0]
    A =
    0 -2 -1
    -2 0 3
    1 -3 0
    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements:
    >> A=[6 -3 8;3 1 7;-8 -7 4],B=[0 -3 8;3 0 7;-8 -7 0]
    A =
    6 -3 8
    3 1 7
    -8 -7 4
    B =
    0 -3 8
    3 0 7
    -8 -7 0
    >> A’,B’
    ans =
    6 3 -8
    -3 1 -7
    8 7 4
    ans =
    0 3 -8
    -3 0 -7
    8 7 0
    >> -A’,-B’
    ans =
    -6 -3 8
    3 -1 7
    -8 -7 -4
    ans =
    0 -3 8
    3 0 7
    -8 -7 0
    Kita bisa melihat bahwa A =-At dan B =-Bt. Jadi itu membuktikan bahwa antisimetrik matriks adalah matriks persegi dengan nol pada setiap elemen diagonal.
    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.
    >> A=[0 -4 8;4 0 -5;-8 5 0],B=[0 7 -3;-7 0 6;3 -6 0]
    A =
    0 -4 8
    4 0 -5
    -8 5 0
    B =
    0 7 -3
    -7 0 6
    3 -6 0
    >> C=A+B
    C =
    0 3 5
    -3 0 1
    -5 -1 0
    >> C’
    ans =
    0 -3 -5
    3 0 -1
    5 1 0
    >> -C’
    ans =
    0 3 5
    -3 0 1
    -5 -1 0
    C = -Ct (antisymmetric matrix berarti benar)

  67. NAMA : RIAN HIDAYAH WIHARJA
    NIM : 10.11.4467
    KELAS: S1 TI 1M

    Pembuktian dengan menggunakan Matlab 7.10

    1. Example of antisymmetric matrix:

    >> A=[0 -2 -1;-2 0 3;1 -3 0]

    A =

    0 -2 -1
    -2 0 3
    1 -3 0

    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements:

    >> A=[6 -3 8;3 1 7;-8 -7 4],B=[0 -3 8;3 0 7;-8 -7 0]

    A =

    6 -3 8
    3 1 7
    -8 -7 4

    B =

    0 -3 8
    3 0 7
    -8 -7 0

    >> A’,B’

    ans =

    6 3 -8
    -3 1 -7
    8 7 4

    ans =

    0 3 -8
    -3 0 -7
    8 7 0

    >> -A’,-B’

    ans =

    -6 -3 8
    3 -1 7
    -8 -7 -4

    ans =

    0 -3 8
    3 0 7
    -8 -7 0

    Kita bisa melihat bahwa A =-At dan B =-Bt. Jadi itu membuktikan bahwa antisimetrik matriks adalah matriks persegi dengan nol pada setiap elemen diagonal.

    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.

    >> A=[0 -4 8;4 0 -5;-8 5 0],B=[0 7 -3;-7 0 6;3 -6 0]

    A =

    0 -4 8
    4 0 -5
    -8 5 0

    B =

    0 7 -3
    -7 0 6
    3 -6 0

    >> C=A+B

    C =

    0 3 5
    -3 0 1
    -5 -1 0

    >> C’

    ans =

    0 -3 -5
    3 0 -1
    5 1 0

    >> -C’

    ans =

    0 3 5
    -3 0 1
    -5 -1 0

    C = -Ct antisymmetric matrix berarti benar

  68. Nama : Rut Merilene H
    NIM : 10.11.4474
    Kelas : S1 TI 1M

    1. Example of antisymmetric matrix:

    0 -2 3
    A= 2 0 -1
    -2 3 0

    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements.
    4 -3 1 0 -4 3
    A= 3 5 -2 B= 4 0 -1
    -1 2 3 -3 1 0

    4 3 -1 0 4 -3
    At= -3 3 2 Bt= -4 0 1
    1-2 5 3 -1 0

    -4 3 1 0 -4 3
    -At=3 -3 -2 -Bt=4 0 -1
    -1 2 -5 -3 1 0

    Kita bisa melihat bahwa A =-At dan B =-Bt. Jadi itu membuktikan bahwa antisimetrik matriks adalah matriks persegi dengan nol pada setiap elemen diagonal.

    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.

    0 -2 1 0 -3 1
    A= 2 0 -3 B= 3 0 -2
    -1 3 0 -1 2 0

    0+0 -3+(-2) 1+1
    C=A+B= 2+3 0+0 -3+(-2)
    -1+(-1) 3+2 0+0

    0 -5 2
    = 5 0 -5
    -2 5 0

    0 5 -2
    Ct= -5 0 5
    2 -5 0

    0 -5 2
    -Ct= 5 0 -5
    -2 5 0
    C = -Ct (antisymmetric matrix)

  69. Nama : Alan Darmasaputra
    NIM : 10.11.4495
    Kelas : S1-TI-1M

    Pembuktian dengan menggunakan Matlab 7.10

    1. Example of antisymmetric matrix:

    >> A=[0 -2 -1;-2 0 3;1 -3 0]

    A =

    0 -2 -1
    -2 0 3
    1 -3 0

    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements:

    >> A=[6 -3 8;3 1 7;-8 -7 4],B=[0 -3 8;3 0 7;-8 -7 0]

    A =

    6 -3 8
    3 1 7
    -8 -7 4

    B =

    0 -3 8
    3 0 7
    -8 -7 0

    >> A’,B’

    ans =

    6 3 -8
    -3 1 -7
    8 7 4

    ans =

    0 3 -8
    -3 0 -7
    8 7 0

    >> -A’,-B’

    ans =

    -6 -3 8
    3 -1 7
    -8 -7 -4

    ans =

    0 -3 8
    3 0 7
    -8 -7 0

    Kita bisa melihat bahwa A =-At dan B =-Bt. Jadi itu membuktikan bahwa antisimetrik matriks adalah matriks persegi dengan nol pada setiap elemen diagonal.

    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.

    >> A=[0 -4 8;4 0 -5;-8 5 0],B=[0 7 -3;-7 0 6;3 -6 0]

    A =

    0 -4 8
    4 0 -5
    -8 5 0

    B =

    0 7 -3
    -7 0 6
    3 -6 0

    >> C=A+B

    C =

    0 3 5
    -3 0 1
    -5 -1 0

    >> C’

    ans =

    0 -3 -5
    3 0 -1
    5 1 0

    >> -C’

    ans =

    0 3 5
    -3 0 1
    -5 -1 0

    C = -Ct antisymmetric matrix berarti benar

  70. Nama :MUHAMMAD USMAN ROSYIDI
    Nim : 10.11.4489
    Kelas : S1-TI-1M

    1. Example of antisymmetric matrix:

    0 4 5
    A = -4 0 -8
    -5 8 0

    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements.

    6 -3 8 0 -2 6
    A = 3 1 6 B = 2 0 6
    8 -6 4 -6 -6 0

    7 3 -8 0 2 -4
    At = -3 1 -4 Bt = -2 0 -7
    8 4 4 4 7 0

    -6 -3 8 0 -2 7
    -At = 3 -1 7 -Bt = 2 0 6
    -8 -7 -4 -7 -6 0

    Kita bisa melihat bahwa A =-At dan B =-Bt. Jadi itu membuktikan bahwa antisimetrik matriks adalah matriks persegi dengan nol pada setiap elemen diagonal.

    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.

    0 -4 8 0 7 -9
    A = 4 0 -5 , B = -7 0 8
    -8 5 0 9 -8 0

    0+0 -4+7 8+(-3)
    C = A + B = 4+(-7) 0+0 -5+6
    -8+3 5+(-6) 0+0

    0 3 5
    = -3 0 1
    -5 -1 0

    0 -3 6
    Ct = 3 0 4
    -6 -4 0

    0 3 7
    -Ct = -3 0 -2
    -7 2 0

    C = -Ct

  71. Nama :MUHAMMAD USMAN ROSYIDI
    Nim : 10.11.4489
    Kelas : S1-TI-1M

    1. Example of antisymmetric matrix:

    0 4 5
    A = -4 0 -8
    -5 8 0

    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements.

    6 -3 8 0 -2 6
    A = 3 1 6 B = 2 0 6
    8 -6 4 -6 -6 0

    7 3 -8 0 2 -4
    At = -3 1 -4 Bt = -2 0 -7
    8 4 4 4 7 0

    -6 -3 8 0 -2 7
    -At = 3 -1 7 -Bt = 2 0 6
    -8 -7 -4 -7 -6 0

    Kita bisa melihat bahwa A =-At dan B =-Bt. Jadi itu membuktikan bahwa antisimetrik matriks adalah matriks persegi dengan nol pada setiap elemen diagonal.

    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.

    0 -4 8 0 7 -9
    A = 4 0 -5 , B = -7 0 8
    -8 5 0 9 -8 0

    0+0 -4+7 8+(-3)
    C = A + B = 4+(-7) 0+0 -5+6
    -8+3 5+(-6) 0+0

    0 3 5
    = -3 0 1
    -5 -1 0

    0 -3 6
    Ct = 3 0 4
    -6 -4 0

    0 3 7
    -Ct = -3 0 -2
    -7 2 0

    C = -Ct (antisymmetric matrix)

  72. Nama :MUHAMMAD USMAN ROSYIDI
    Nim : 10.11.4489
    Kelas : S1-TI-1M

    1. Example of antisymmetric matrix:

    0 4 5
    A = -4 0 -8
    -5 8 0

    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements.

    6 -3 8 0 -2 7
    A = 3 1 7 B = 2 0 6
    8 -7 4 -7 -6 0

    6 3 -8 0 2 -7
    At = -3 1 -7 Bt = -2 0 -6
    8 7 4 7 6 0

    -6 -3 8 0 -2 7
    -At = 3 -1 7 -Bt = 2 0 6
    -8 -7 -4 -7 -6 0

    Kita bisa melihat bahwa A =-At dan B =-Bt. Jadi itu membuktikan bahwa antisimetrik matriks adalah matriks persegi dengan nol pada setiap elemen diagonal.

    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.

    0 -4 8 0 7 -3
    A = 4 0 -5 , B = -7 0 6
    -8 5 0 3 -6 0

    0+0 -4+7 8+(-3)
    C = A + B = 4+(-7) 0+0 -5+6
    -8+3 5+(-6) 0+0

    0 3 5
    = -3 0 1
    -5 -1 0

    0 -3 6
    Ct = 3 0 4
    -6 -4 0

    0 3 7
    -Ct = -3 0 -2
    -7 2 0

    C = -Ct (antisymmetric matrix)

  73. Nama :MUHAMMAD USMAN ROSYIDI
    Nim : 10.11.4489
    Kelas : S1-TI-1M

    1. Example of antisymmetric matrix:

    0 4 -3
    A = -4 0 6
    3 -6 0

    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements.

    6 -3 8 0 -2 7
    A = 3 1 7 B = 2 0 6
    8 -7 4 -7 -6 0

    6 3 -8 0 2 -7
    At = -3 1 -7 Bt = -2 0 -6
    8 7 4 7 6 0

    -6 -3 8 0 -2 7
    -At = 3 -1 7 -Bt = 2 0 6a
    -8 -7 -4 -7 -6 0

    Kita bisa melihat bahwa A =-At dan B =-Bt. Jadi itu membuktikan bahwa antisimetrik matriks adalah matriks persegi dengan nol pada setiap elemen diagonal.

    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.

    0 -4 8 0 7 -3
    A = 4 0 -5 , B = -7 0 6
    -8 5 0 3 -6 0

    0+0 -4+7 8+(-3)
    C = A + B = 4+(-7) 0+0 -5+6
    -8+3 5+(-6) 0+0

    0 3 5
    = -3 0 1
    -5 -1 0

    0 -3 -5
    Ct = 3 0 -1
    5 1 0

    0 3 5
    -Ct = -3 0 1
    -5 -1 0

    C = -Ct (antisymmetric matrix)

  74. Nama : M.USMAN ROSYIDI
    Nim : 10.11.4489
    Kelas : S1-TI-1M

    1. Example of antisymmetric matrix:

    0 4 -3
    A = -4 0 6
    3 -6 0

    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements.

    6 -3 8 0 -2 7
    A = 3 1 7 B = 2 0 6
    8 -7 4 -7 -6 0

    6 3 -8 0 2 -7
    At = -3 1 -7 Bt = -2 0 -6
    8 7 4 7 6 0

    -6 -3 8 0 -2 7
    -At = 3 -1 7 -Bt = 2 0 6
    -8 -7 -4 -7 -6 0

    Kita bisa melihat bahwa A =-At dan B =-Bt. Jadi itu membuktikan bahwa antisimetrik matriks adalah matriks persegi dengan nol pada setiap elemen diagonal.

    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.

    0 -4 8 0 7 -3
    A = 4 0 -5 , B = -7 0 6
    -8 5 0 3 -6 0

    0+0 -4+7 8+(-3)
    C = A + B = 4+(-7) 0+0 -5+6
    -8+3 5+(-6) 0+0

    0 3 5
    = -3 0 1
    -5 -1 0

    0 -3 -5
    Ct = 3 0 -1
    5 1 0

    0 3 5
    -Ct = -3 0 1
    -5 -1 0

    C = -Ct (antisymmetric matrix)

  75. Nama :MUHAMMAD USMAN ROSYIDI
    Nim : 10.11.4489
    Kelas : S1-TI-1M

    1. Example of antisymmetric matrix:

    0 4 -3
    A = -4 0 6
    3 -6 0

    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements.

    6 -3 8 0 -2 7
    A = 3 1 7 B = 2 0 6
    8 -7 4 -7 -6 0

    6 3 -8 0 2 -7
    At = -3 1 -7 Bt = -2 0 -6
    8 7 4 7 6 0

    -6 -3 8 0 -2 7
    -At = 3 -1 7 -Bt = 2 0 6
    -8 -7 -4 -7 -6 0

    Kita bisa melihat bahwa A =-At dan B =-Bt. Jadi itu membuktikan bahwa antisimetrik matriks adalah matriks persegi dengan nol pada setiap elemen diagonal.

    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.

    0 -4 8 0 7 -3
    A = 4 0 -5 , B = -7 0 6
    -8 5 0 3 -6 0

    0+0 -4+7 8+(-3)
    C = A + B = 4+(-7) 0+0 -5+6
    -8+3 5+(-6) 0+0

    0 3 5
    = -3 0 1
    -5 -1 0

    0 -3 -5
    Ct = 3 0 -1
    5 1 0

    0 3 5
    -Ct = -3 0 1
    -5 -1 0

    C = -Ct (antisymmetric matrix)

  76. Nama : MUHAMMAD USMAN ROSYIDI
    Nim : 10.11.4489
    Kelas : S1-TI-1M

    1. Example of antisymmetric matrix:

    0 4 -3
    A = -4 0 6
    3 -6 0

    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements.

    6 -3 8 0 -2 7
    A = 3 1 7 B = 2 0 6
    8 -7 4 -7 -6 0

    6 3 -8 0 2 -7
    At = -3 1 -7 Bt = -2 0 -6
    8 7 4 7 6 0

    -6 -3 8 0 -2 7
    -At = 3 -1 7 -Bt = 2 0 6
    -8 -7 -4 -7 -6 0

    Kita bisa melihat bahwa A =-At dan B =-Bt. Jadi itu membuktikan bahwa antisimetrik matriks adalah matriks persegi dengan nol pada setiap elemen diagonal.

    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.

    0 -4 8 0 7 -3
    A = 4 0 -5 , B = -7 0 6
    -8 5 0 3 -6 0

    0+0 -4+7 8+(-3)
    C = A + B = 4+(-7) 0+0 -5+6
    -8+3 5+(-6) 0+0

    0 3 5
    = -3 0 1
    -5 -1 0

    0 -3 -5
    Ct = 3 0 -1
    5 1 0

    0 3 5
    -Ct = -3 0 1
    -5 -1 0

    C = -Ct (antisymmetric matrix)

  77. M.Ervan Wirawan
    10.11.4513

    1. Example of antisymmetric matrix:

    0 4 -3
    A = -4 0 6
    3 -6 0

    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements.

    6 -3 8 0 -2 7
    A = 3 1 7 B = 2 0 6
    -8 -7 4 -7 -6 0

    6 3 -8 0 2 -7
    At = -3 1 -7 Bt = -2 0 -6
    8 7 4 7 6 0

    -6 -3 8 0 -2 7
    -At = 3 -1 7 -Bt = 2 0 6
    -8 -7 -4 -7 -6 0

    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.

    0 -4 8 0 7 -3
    A = 4 0 -5 , B = -7 0 6
    -8 5 0 3 -6 0

    0+0 -4+7 8+(-3)
    C = A + B = 4+(-7) 0+0 -5+6
    -8+3 5+(-6) 0+0

    0 3 5
    = -3 0 1
    -5 -1 0

    0 -3 -5
    Ct = 3 0 -1
    5 1 0

    0 3 5
    -Ct = -3 0 1
    -5 -1 0

    C = -Ct (antisymmetric matrix)

  78. Nama : pamji ginanjar setiawan
    NIM : 10.11.4484
    Kelas : S1 TI 1M

    Pembuktian dengan menggunakan Matlab 7.10

    1. Example of antisymmetric matrix:

    >> A=[0 -2 -1;-2 0 3;1 -3 0]

    A =

    0 -2 -1
    -2 0 3
    1 -3 0

    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements:

    >> A=[6 -3 8;3 1 7;-8 -7 4],B=[0 -3 8;3 0 7;-8 -7 0]

    A =

    6 -3 8
    3 1 7
    -8 -7 4

    B =

    0 -3 8
    3 0 7
    -8 -7 0

    >> A’,B’

    ans =

    6 3 -8
    -3 1 -7
    8 7 4

    ans =

    0 3 -8
    -3 0 -7
    8 7 0

    >> -A’,-B’

    ans =

    -6 -3 8
    3 -1 7
    -8 -7 -4

    ans =

    0 -3 8
    3 0 7
    -8 -7 0

    Kita bisa melihat bahwa A =-At dan B =-Bt. Jadi itu membuktikan bahwa antisimetrik matriks adalah matriks persegi dengan nol pada setiap elemen diagonal.

    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.

    >> A=[0 -4 8;4 0 -5;-8 5 0],B=[0 7 -3;-7 0 6;3 -6 0]

    A =

    0 -4 8
    4 0 -5
    -8 5 0

    B =

    0 7 -3
    -7 0 6
    3 -6 0

    >> C=A+B

    C =

    0 3 5
    -3 0 1
    -5 -1 0

    >> C’

    ans =

    0 -3 -5
    3 0 -1
    5 1 0

    >> -C’

    ans =

    0 3 5
    -3 0 1
    -5 -1 0

    C = -Ct (antisymmetric matrix berarti bener)

  79. Nama : panji ginanjar setiawan
    Nim : 10.11.4584
    Kelas : S1-TI-1M

    1. Example of antisymmetric matrix:

    0 4 -3
    A = -4 0 6
    3 -6 0

    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements.

    6 -3 8 0 -2 7
    A = 3 1 7 B = 2 0 6
    8 -7 4 -7 -6 0

    6 3 -8 0 2 -7
    At = -3 1 -7 Bt = -2 0 -6
    8 7 4 7 6 0

    -6 -3 8 0 -2 7
    -At = 3 -1 7 -Bt = 2 0 6
    -8 -7 -4 -7 -6 0

    Kita bisa melihat bahwa A =-At dan B =-Bt. Jadi itu membuktikan bahwa antisimetrik matriks adalah matriks persegi dengan nol pada setiap elemen diagonal.

    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.

    0 -4 8 0 7 -3
    A = 4 0 -5 , B = -7 0 6
    -8 5 0 3 -6 0

    0+0 -4+7 8+(-3)
    C = A + B = 4+(-7) 0+0 -5+6
    -8+3 5+(-6) 0+0

    0 3 5
    = -3 0 1
    -5 -1 0

    0 -3 -5
    Ct = 3 0 -1
    5 1 0

    0 3 5
    -Ct = -3 0 1
    -5 -1 0

    C = -Ct (antisymmetric matrix)

  80. Nama : Panji ginanjar setiawan
    NIM : 10.11.4484
    Kelas : S1-TI-1M

    1. Example of antisymmetric matrix:

    0 3 -2
    A = -3 0 1
    2 -1 0

    2. Prove that antisymmetric matrix is a square matrix with

    zero on each diagonal elements.
    Antisymmetric matrix is an anti of symmetric matrix, with (A= -At ). That mean the matrix is equal to its transpose, but each element of the transposed matrix has an opposite sign of the matrix.

    Here are two examples of symmetric matrix, one with zero on each diagonal elements.

    8 -4 9 0 -4 9
    A = 4 5 6 B = 4 0 6
    -9 -6 3 -9 -6 0

    8 4 -9 0 4 -9
    At = -4 5 -6 Bt = -4 0 -6
    9 6 3 9 6 0

    -8 -4 9 0 -4 9
    -At = 4 -5 6 -Bt = 4 0 6
    -9 -6 -3 -9 -6 0

    We could see that A != -At and B = -Bt. So it’s proved that antisymmetric matrix is a square matrix with zero on each diagonal elements.

    3. Prove that sum of two antisymmetric matrix is an

    antisymmetric matrix.

    0 -4 9 0 3 -8
    A = 4 0 -6 , B = -3 0 7
    -9 6 0 8 -7 0

    0+0 -4+3 9+(-8)
    C = A + B = 4+(-3) 0+0 -6+7
    -9+8 6+(-7) 0+0

    0 -1 1
    = 1 0 1
    -1 -1 0

    0 1 -1
    Ct = -1 0 -1
    1 1 0

    0 -1 1
    -Ct = 1 0 1
    -1 -1 0

    C = -Ct (antisymmetric matrix)

  81. Nama : panji ginanjar setiawan
    NIM : 10.11.4484
    Kelas : S1 TI 1M

    Pembuktian dengan menggunakan Matlab 7.10

    1. Example of antisymmetric matrix:

    >> A=[0 -2 -1;-2 0 3;1 -3 0]

    A =

    0 -2 -1
    -2 0 3
    1 -3 0

    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements:

    >> A=[6 -3 8;3 1 7;-8 -7 4],B=[0 -3 8;3 0 7;-8 -7 0]

    A =

    6 -3 8
    3 1 7
    -8 -7 4

    B =

    0 -3 8
    3 0 7
    -8 -7 0

    >> A’,B’

    ans =

    6 3 -8
    -3 1 -7
    8 7 4

    ans =

    0 3 -8
    -3 0 -7
    8 7 0

    >> -A’,-B’

    ans =

    -6 -3 8
    3 -1 7
    -8 -7 -4

    ans =

    0 -3 8
    3 0 7
    -8 -7 0

    Kita bisa melihat bahwa A =-At dan B =-Bt. Jadi itu membuktikan bahwa antisimetrik matriks adalah matriks persegi dengan nol pada setiap elemen diagonal.

    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.

    >> A=[0 -4 8;4 0 -5;-8 5 0],B=[0 7 -3;-7 0 6;3 -6 0]

    A =

    0 -4 8
    4 0 -5
    -8 5 0

    B =

    0 7 -3
    -7 0 6
    3 -6 0

    >> C=A+B

    C =

    0 3 5
    -3 0 1
    -5 -1 0

    >> C’

    ans =

    0 -3 -5
    3 0 -1
    5 1 0

    >> -C’

    ans =

    0 3 5
    -3 0 1
    -5 -1 0

    C = -Ct (antisymmetric matrix berarti bener)

  82. Nama : Faldi Dwi Hastiya
    NIM : 10.11.4523
    Kelas : S1 TI 1M

    Pembuktian dengan menggunakan Matlab 7.10

    1. Example of antisymmetric matrix:

    >> A=[0 -2 -1;-2 0 3;1 -3 0]

    A =

    0 -2 -1
    -2 0 3
    1 -3 0

    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements:

    >> A=[6 -3 8;3 1 7;-8 -7 4],B=[0 -3 8;3 0 7;-8 -7 0]

    A =

    6 -3 8
    3 1 7
    -8 -7 4

    B =

    0 -3 8
    3 0 7
    -8 -7 0

    >> A’,B’

    ans =

    6 3 -8
    -3 1 -7
    8 7 4

    ans =

    0 3 -8
    -3 0 -7
    8 7 0

    >> -A’,-B’

    ans =

    -6 -3 8
    3 -1 7
    -8 -7 -4

    ans =

    0 -3 8
    3 0 7
    -8 -7 0

    Kita bisa melihat bahwa A =-At dan B =-Bt. Jadi itu membuktikan bahwa antisimetrik matriks adalah matriks persegi dengan nol pada setiap elemen diagonal.

    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.

    >> A=[0 -4 8;4 0 -5;-8 5 0],B=[0 7 -3;-7 0 6;3 -6 0]

    A =

    0 -4 8
    4 0 -5
    -8 5 0

    B =

    0 7 -3
    -7 0 6
    3 -6 0

    >> C=A+B

    C =

    0 3 5
    -3 0 1
    -5 -1 0

    >> C’

    ans =

    0 -3 -5
    3 0 -1
    5 1 0

    >> -C’

    ans =

    0 3 5
    -3 0 1
    -5 -1 0

    C = -Ct (antisymmetric matrix berarti bener)

  83. Nama : Eko Whyu Nugroho
    NIM : 10.11.4468
    Kelas : S1 TI 1M

    Pembuktian dengan menggunakan Matlab 7.10

    1. Example of antisymmetric matrix:

    >> A=[0 -2 -1;-2 0 3;1 -3 0]

    A =

    0 -2 -1
    -2 0 3
    1 -3 0

    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements:

    >> A=[6 -3 8;3 1 7;-8 -7 4],B=[0 -3 8;3 0 7;-8 -7 0]

    A =

    6 -3 8
    3 1 7
    -8 -7 4

    B =

    0 -3 8
    3 0 7
    -8 -7 0

    >> A’,B’

    ans =

    6 3 -8
    -3 1 -7
    8 7 4

    ans =

    0 3 -8
    -3 0 -7
    8 7 0

    >> -A’,-B’

    ans =

    -6 -3 8
    3 -1 7
    -8 -7 -4

    ans =

    0 -3 8
    3 0 7
    -8 -7 0

    Kita bisa melihat bahwa A =-At dan B =-Bt. Jadi itu membuktikan bahwa antisimetrik matriks adalah matriks persegi dengan nol pada setiap elemen diagonal.

    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.

    >> A=[0 -4 8;4 0 -5;-8 5 0],B=[0 7 -3;-7 0 6;3 -6 0]

    A =

    0 -4 8
    4 0 -5
    -8 5 0

    B =

    0 7 -3
    -7 0 6
    3 -6 0

    >> C=A+B

    C =

    0 3 5
    -3 0 1
    -5 -1 0

    >> C’

    ans =

    0 -3 -5
    3 0 -1
    5 1 0

    >> -C’

    ans =

    0 3 5
    -3 0 1
    -5 -1 0

    C = -Ct (antisymmetric matrix berarti bener)

  84. Nama : Beny Viktor
    NIM : 10.11.4480
    Kelas : S1 TI 1M

    Pembuktian dengan menggunakan Matlab 7.10

    1. Example of antisymmetric matrix:

    >> A=[0 -2 -1;-2 0 3;1 -3 0]

    A =

    0 -2 -1
    -2 0 3
    1 -3 0

    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements:

    >> A=[6 -3 8;3 1 7;-8 -7 4],B=[0 -3 8;3 0 7;-8 -7 0]

    A =

    6 -3 8
    3 1 7
    -8 -7 4

    B =

    0 -3 8
    3 0 7
    -8 -7 0

    >> A’,B’

    ans =

    6 3 -8
    -3 1 -7
    8 7 4

    ans =

    0 3 -8
    -3 0 -7
    8 7 0

    >> -A’,-B’

    ans =

    -6 -3 8
    3 -1 7
    -8 -7 -4

    ans =

    0 -3 8
    3 0 7
    -8 -7 0

    Kita bisa melihat bahwa A =-At dan B =-Bt. Jadi itu membuktikan bahwa antisimetrik matriks adalah matriks persegi dengan nol pada setiap elemen diagonal.

    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.

    >> A=[0 -4 8;4 0 -5;-8 5 0],B=[0 7 -3;-7 0 6;3 -6 0]

    A =

    0 -4 8
    4 0 -5
    -8 5 0

    B =

    0 7 -3
    -7 0 6
    3 -6 0

    >> C=A+B

    C =

    0 3 5
    -3 0 1
    -5 -1 0

    >> C’

    ans =

    0 -3 -5
    3 0 -1
    5 1 0

    >> -C’

    ans =

    0 3 5
    -3 0 1
    -5 -1 0

    C = -Ct (antisymmetric matrix berarti bener)

  85. Nama : Dwi Prasetyo Wibowo
    NIM : 10.11.4471
    Kelas : S1 TI 1M

    Pembuktian dengan menggunakan Matlab 7.10

    1. Example of antisymmetric matrix:

    >> A=[0 -2 -1;-2 0 3;1 -3 0]

    A =

    0 -2 -1
    -2 0 3
    1 -3 0

    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements:

    >> A=[6 -3 8;3 1 7;-8 -7 4],B=[0 -3 8;3 0 7;-8 -7 0]

    A =

    6 -3 8
    3 1 7
    -8 -7 4

    B =

    0 -3 8
    3 0 7
    -8 -7 0

    >> A’,B’

    ans =

    6 3 -8
    -3 1 -7
    8 7 4

    ans =

    0 3 -8
    -3 0 -7
    8 7 0

    >> -A’,-B’

    ans =

    -6 -3 8
    3 -1 7
    -8 -7 -4

    ans =

    0 -3 8
    3 0 7
    -8 -7 0

    Kita bisa melihat bahwa A =-At dan B =-Bt. Jadi itu membuktikan bahwa antisimetrik matriks adalah matriks persegi dengan nol pada setiap elemen diagonal.

    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.

    >> A=[0 -4 8;4 0 -5;-8 5 0],B=[0 7 -3;-7 0 6;3 -6 0]

    A =

    0 -4 8
    4 0 -5
    -8 5 0

    B =

    0 7 -3
    -7 0 6
    3 -6 0

    >> C=A+B

    C =

    0 3 5
    -3 0 1
    -5 -1 0

    >> C’

    ans =

    0 -3 -5
    3 0 -1
    5 1 0

    >> -C’

    ans =

    0 3 5
    -3 0 1
    -5 -1 0

    C = -Ct (antisymmetric matrix berarti bener)

  86. Nama : Dwi Prosetyo Wibowo
    NIM : 10.11.4471
    Kelas : S1 TI 1M

    Pembuktian dengan menggunakan Matlab 7.10

    1. Example of antisymmetric matrix:

    >> A=[0 -2 -1;-2 0 3;1 -3 0]

    A =

    0 -2 -1
    -2 0 3
    1 -3 0

    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements:

    >> A=[6 -3 8;3 1 7;-8 -7 4],B=[0 -3 8;3 0 7;-8 -7 0]

    A =

    6 -3 8
    3 1 7
    -8 -7 4

    B =

    0 -3 8
    3 0 7
    -8 -7 0

    >> A’,B’

    ans =

    6 3 -8
    -3 1 -7
    8 7 4

    ans =

    0 3 -8
    -3 0 -7
    8 7 0

    >> -A’,-B’

    ans =

    -6 -3 8
    3 -1 7
    -8 -7 -4

    ans =

    0 -3 8
    3 0 7
    -8 -7 0

    Kita bisa melihat bahwa A =-At dan B =-Bt. Jadi itu membuktikan bahwa antisimetrik matriks adalah matriks persegi dengan nol pada setiap elemen diagonal.

    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.

    >> A=[0 -4 8;4 0 -5;-8 5 0],B=[0 7 -3;-7 0 6;3 -6 0]

    A =

    0 -4 8
    4 0 -5
    -8 5 0

    B =

    0 7 -3
    -7 0 6
    3 -6 0

    >> C=A+B

    C =

    0 3 5
    -3 0 1
    -5 -1 0

    >> C’

    ans =

    0 -3 -5
    3 0 -1
    5 1 0

    >> -C’

    ans =

    0 3 5
    -3 0 1
    -5 -1 0

    C = -Ct (antisymmetric matrix berarti bener)

  87. Nama : Aurelius N Taja
    NIM : 10.11.4473
    Kelas : 1M

    Pembuktian dengan menggunakan Matlab 7.10

    1. Example of antisymmetric matrix:

    >> A=[0 -2 -1;-2 0 3;1 -3 0]

    A =

    0 -2 -1
    -2 0 3
    1 -3 0

    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements:

    >> A=[6 -3 8;3 1 7;-8 -7 4],B=[0 -3 8;3 0 7;-8 -7 0]

    A =

    6 -3 8
    3 1 7
    -8 -7 4

    B =

    0 -3 8
    3 0 7
    -8 -7 0

    >> A’,B’

    ans =

    6 3 -8
    -3 1 -7
    8 7 4

    ans =

    0 3 -8
    -3 0 -7
    8 7 0

    >> -A’,-B’

    ans =

    -6 -3 8
    3 -1 7
    -8 -7 -4

    ans =

    0 -3 8
    3 0 7
    -8 -7 0

    Kita bisa melihat bahwa A =-At dan B =-Bt. Jadi itu membuktikan bahwa antisimetrik matriks adalah matriks persegi dengan nol pada setiap elemen diagonal.

    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.

    >> A=[0 -4 8;4 0 -5;-8 5 0],B=[0 7 -3;-7 0 6;3 -6 0]

    A =

    0 -4 8
    4 0 -5
    -8 5 0

    B =

    0 7 -3
    -7 0 6
    3 -6 0

    >> C=A+B

    C =

    0 3 5
    -3 0 1
    -5 -1 0

    >> C’

    ans =

    0 -3 -5
    3 0 -1
    5 1 0

    >> -C’

    ans =

    0 3 5
    -3 0 1
    -5 -1 0

    C = -Ct (antisymmetric matrix berarti bener)

  88. nama : panji ginanjar.s
    nim : 10.11.4484
    kelas : s1 ti 1m
    1. Example of antisymmetric matrix:

    0 4 -3
    A = -4 0 6
    3 -6 0

    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements.

    6 -3 8 0 -2 7
    A = 3 1 7 B = 2 0 6
    8 -7 4 -7 -6 0

    6 3 -8 0 2 -7
    At = -3 1 -7 Bt = -2 0 -6
    8 7 4 7 6 0

    -6 -3 8 0 -2 7
    -At = 3 -1 7 -Bt = 2 0 6
    -8 -7 -4 -7 -6 0

    Kita bisa melihat bahwa A =-At dan B =-Bt. Jadi itu membuktikan bahwa antisimetrik matriks adalah matriks persegi dengan nol pada setiap elemen diagonal.

    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.

    0 -4 8 0 7 -3
    A = 4 0 -5 , B = -7 0 6
    -8 5 0 3 -6 0

    0+0 -4+7 8+(-3)
    C = A + B = 4+(-7) 0+0 -5+6
    -8+3 5+(-6) 0+0

    0 3 5
    = -3 0 1
    -5 -1 0

    0 -3 -5
    Ct = 3 0 -1
    5 1 0

    0 3 5
    -Ct = -3 0 1
    -5 -1 0

    C = -Ct (antisymmetric matrix)

  89. NAMA : PANJI GINANJAR.S
    NIM : 10.11.4484
    KELAS :S1 TI 1M

    1. Example of antisymmetric matrix:

    0 4 -2
    A = -3 2 5
    1 -5 0

    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements.

    Antisymmetric matrix is an anti of symmetric matrix, with (A= -At ). That mean the matrix is equal to its transpose, but each element of the transposed matrix has an opposite sign of the matrix.

    Here are two examples of symmetric matrix, one with zero on each diagonal elements.

    6 -2 1 6 5 9
    A = 4 2 5 B = -2 0 -1
    -8 -3 2 1 -4 2

    -6 2 1 -6 -5 -9
    At = -4 -2 -5 Bt = 2 0 1
    8 3 -2 -1 4 -2

    6 -2 1 6 5 9
    -At = 4 2 5 -Bt = -2 0 -1
    -8 -3 2 1 -4 2

    We could see that A != -At and B = -Bt. So it’s proved that antisymmetric matrix is a square matrix with zero on each diagonal elements.

    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.

    1 2 1 4 -2 -5
    Let A = 3 0 3 , B = -1 0 4
    -2 3 0 5 -4 0

    1+4 2+(-2) 1+(-5)
    C = A + B = 3+(-1) 0+0 3+4
    -2+5 3+(-4) 0+0

    5 0 -4
    = 2 0 7
    3 -1 0

    5 0 -4
    Ct = 2 0 7
    3 -1 0

    -5 0 4
    -Ct = -2 0 -7
    -3 1 0

    C = -Ct (antisymmetric matrix)

  90. nama:panji ginanjar setiawan
    NIM : 10.11.4484
    kelas:s1 TI 1M
    1. Example of antisymmetric matrix:

    0 4 -2
    A = -3 2 5
    1 -5 0

    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements.

    Antisymmetric matrix is an anti of symmetric matrix, with (A= -At ). That mean the matrix is equal to its transpose, but each element of the transposed matrix has an opposite sign of the matrix.

    Here are two examples of symmetric matrix, one with zero on each diagonal elements.

    6 -2 1 6 5 9
    A = 4 2 5 B = -2 0 -1
    -8 -3 2 1 -4 2

    -6 2 1 -6 -5 -9
    At = -4 -2 -5 Bt = 2 0 1
    8 3 -2 -1 4 -2

    6 -2 1 6 5 9
    -At = 4 2 5 -Bt = -2 0 -1
    -8 -3 2 1 -4 2

    We could see that A != -At and B = -Bt. So it’s proved that antisymmetric matrix is a square matrix with zero on each diagonal elements.

    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.

    1 2 1 4 -2 -5
    Let A = 3 0 3 , B = -1 0 4
    -2 3 0 5 -4 0

    1+4 2+(-2) 1+(-5)
    C = A + B = 3+(-1) 0+0 3+4
    -2+5 3+(-4) 0+0

    5 0 -4
    = 2 0 7
    3 -1 0

    5 0 -4
    Ct = 2 0 7
    3 -1 0

    -5 0 4
    -Ct = -2 0 -7
    -3 1 0

    C = -Ct (antisymmetric matrix)

  91. Nama : Banter Prayogo
    Nim : 10.11.4470
    Kelas : S1-TI-1M

    1. Example of antisymmetric matrix:

    0 4 -3
    A = -4 0 6
    3 -6 0

    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements.

    6 -3 8 0 -2 7
    A = 3 1 7 B = 2 0 6
    8 -7 4 -7 -6 0

    6 3 -8 0 2 -7
    At = -3 1 -7 Bt = -2 0 -6
    8 7 4 7 6 0

    -6 -3 8 0 -2 7
    -At = 3 -1 7 -Bt = 2 0 6
    -8 -7 -4 -7 -6 0

    Kita bisa melihat bahwa A =-At dan B =-Bt. Jadi itu membuktikan bahwa antisimetrik matriks adalah matriks persegi dengan nol pada setiap elemen diagonal.

    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.

    0 -4 8 0 7 -3
    A = 4 0 -5 , B = -7 0 6
    -8 5 0 3 -6 0

    0+0 -4+7 8+(-3)
    C = A + B = 4+(-7) 0+0 -5+6
    -8+3 5+(-6) 0+0

    0 3 5
    = -3 0 1
    -5 -1 0

    0 -3 -5
    Ct = 3 0 -1
    5 1 0

    0 3 5
    -Ct = -3 0 1
    -5 -1 0

    C = -Ct (antisymmetric matrix)

  92. Nama : Adnan Dwipa Hanggoro
    Nim : 10.11.4539
    Kelas : S1-TI-1M

    1. Example of antisymmetric matrix:

    0 4 -3
    A = -4 0 6
    3 -6 0

    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements.

    6 -3 8 0 -2 7
    A = 3 1 7 B = 2 0 6
    8 -7 4 -7 -6 0

    6 3 -8 0 2 -7
    At = -3 1 -7 Bt = -2 0 -6
    8 7 4 7 6 0

    -6 -3 8 0 -2 7
    -At = 3 -1 7 -Bt = 2 0 6
    -8 -7 -4 -7 -6 0

    Kita bisa melihat bahwa A =-At dan B =-Bt. Jadi itu membuktikan bahwa antisimetrik matriks adalah matriks persegi dengan nol pada setiap elemen diagonal.

    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.

    0 -4 8 0 7 -3
    A = 4 0 -5 , B = -7 0 6
    -8 5 0 3 -6 0

    0+0 -4+7 8+(-3)
    C = A + B = 4+(-7) 0+0 -5+6
    -8+3 5+(-6) 0+0

    0 3 5
    = -3 0 1
    -5 -1 0

    0 -3 -5
    Ct = 3 0 -1
    5 1 0

    0 3 5
    -Ct = -3 0 1
    -5 -1 0

    C = -Ct (antisymmetric matrix)

  93. Nama : Bima Aditya Rahayu
    Nim : 10.11.4476
    Kelas : S1-TI-1M

    1. Example of antisymmetric matrix:

    0 4 -3
    A = -4 0 6
    3 -6 0

    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements.

    6 -3 8 0 -2 7
    A = 3 1 7 B = 2 0 6
    8 -7 4 -7 -6 0

    6 3 -8 0 2 -7
    At = -3 1 -7 Bt = -2 0 -6
    8 7 4 7 6 0

    -6 -3 8 0 -2 7
    -At = 3 -1 7 -Bt = 2 0 6
    -8 -7 -4 -7 -6 0

    Kita bisa melihat bahwa A =-At dan B =-Bt. Jadi itu membuktikan bahwa antisimetrik matriks adalah matriks persegi dengan nol pada setiap elemen diagonal.

    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.

    0 -4 8 0 7 -3
    A = 4 0 -5 , B = -7 0 6
    -8 5 0 3 -6 0

    0+0 -4+7 8+(-3)
    C = A + B = 4+(-7) 0+0 -5+6
    -8+3 5+(-6) 0+0

    0 3 5
    = -3 0 1
    -5 -1 0

    0 -3 -5
    Ct = 3 0 -1
    5 1 0

    0 3 5
    -Ct = -3 0 1
    -5 -1 0

    C = -Ct (antisymmetric matrix)

  94. Nama : Mahasin Ahmad Alfaqh
    Nim : 10.11.4530
    Kelas : S1-TI-1M

    1. Example of antisymmetric matrix:

    0 4 -3
    A = -4 0 6
    3 -6 0

    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements.

    6 -3 8 0 -2 7
    A = 3 1 7 B = 2 0 6
    8 -7 4 -7 -6 0

    6 3 -8 0 2 -7
    At = -3 1 -7 Bt = -2 0 -6
    8 7 4 7 6 0

    -6 -3 8 0 -2 7
    -At = 3 -1 7 -Bt = 2 0 6
    -8 -7 -4 -7 -6 0

    Kita bisa melihat bahwa A =-At dan B =-Bt. Jadi itu membuktikan bahwa antisimetrik matriks adalah matriks persegi dengan nol pada setiap elemen diagonal.

    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.

    0 -4 8 0 7 -3
    A = 4 0 -5 , B = -7 0 6
    -8 5 0 3 -6 0

    0+0 -4+7 8+(-3)
    C = A + B = 4+(-7) 0+0 -5+6
    -8+3 5+(-6) 0+0

    0 3 5
    = -3 0 1
    -5 -1 0

    0 -3 -5
    Ct = 3 0 -1
    5 1 0

    0 3 5
    -Ct = -3 0 1
    -5 -1 0

    C = -Ct (antisymmetric matrix)

  95. Nama : Nur Cholis
    Nim : 10.11.4545
    Kelas : S1-TI-1M

    1. Example of antisymmetric matrix:

    0 4 -3
    A = -4 0 6
    3 -6 0

    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements.

    6 -3 8 0 -2 7
    A = 3 1 7 B = 2 0 6
    8 -7 4 -7 -6 0

    6 3 -8 0 2 -7
    At = -3 1 -7 Bt = -2 0 -6
    8 7 4 7 6 0

    -6 -3 8 0 -2 7
    -At = 3 -1 7 -Bt = 2 0 6
    -8 -7 -4 -7 -6 0

    Kita bisa melihat bahwa A =-At dan B =-Bt. Jadi itu membuktikan bahwa antisimetrik matriks adalah matriks persegi dengan nol pada setiap elemen diagonal.

    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.

    0 -4 8 0 7 -3
    A = 4 0 -5 , B = -7 0 6
    -8 5 0 3 -6 0

    0+0 -4+7 8+(-3)
    C = A + B = 4+(-7) 0+0 -5+6
    -8+3 5+(-6) 0+0

    0 3 5
    = -3 0 1
    -5 -1 0

    0 -3 -5
    Ct = 3 0 -1
    5 1 0

    0 3 5
    -Ct = -3 0 1
    -5 -1 0

    C = -Ct (antisymmetric matrix)

  96. Nama : Muhamad Amirudin Fauzi
    NIM : 10.11.4479
    Kelas : S1-TI-1M

    1. Example of antisymmetric matrix:

    0 4 -3
    A = -4 0 6
    3 -6 0

    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements.

    6 -3 8 0 -2 7
    A = 3 1 7 B = 2 0 6
    8 -7 4 -7 -6 0

    6 3 -8 0 2 -7
    At = -3 1 -7 Bt = -2 0 -6
    8 7 4 7 6 0

    -6 -3 8 0 -2 7
    -At = 3 -1 7 -Bt = 2 0 6
    -8 -7 -4 -7 -6 0

    Kita bisa melihat bahwa A =-At dan B =-Bt. Jadi itu membuktikan bahwa antisimetrik matriks adalah matriks persegi dengan nol pada setiap elemen diagonal.

    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.

    0 -4 8 0 7 -3
    A = 4 0 -5 , B = -7 0 6
    -8 5 0 3 -6 0

    0+0 -4+7 8+(-3)
    C = A + B = 4+(-7) 0+0 -5+6
    -8+3 5+(-6) 0+0

    0 3 5
    = -3 0 1
    -5 -1 0

    0 -3 -5
    Ct = 3 0 -1
    5 1 0

    0 3 5
    -Ct = -3 0 1
    -5 -1 0

    C = -Ct (antisymmetric matrix)

  97. Nama : Muhamad Amirudin Fauzi
    NIM : 10.11.4479
    Kelas : S1- TI – 1M

    1. Example of antisymmetric matrix:

    0 3 -2
    A = -3 0 1
    2 -1 0

    2. Prove that antisymmetric matrix is a square matrix with

    zero on each diagonal elements.
    Antisymmetric matrix is an anti of symmetric matrix, with (A= -At ). That mean the matrix is equal to its transpose, but each element of the transposed matrix has an opposite sign of the matrix.

    Here are two examples of symmetric matrix, one with zero on each diagonal elements.

    8 -4 9 0 -4 9
    A = 4 5 6 B = 4 0 6
    -9 -6 3 -9 -6 0

    8 4 -9 0 4 -9
    At = -4 5 -6 Bt = -4 0 -6
    9 6 3 9 6 0

    -8 -4 9 0 -4 9
    -At = 4 -5 6 -Bt = 4 0 6
    -9 -6 -3 -9 -6 0

    We could see that A != -At and B = -Bt. So it’s proved that antisymmetric matrix is a square matrix with zero on each diagonal elements.

    3. Prove that sum of two antisymmetric matrix is an

    antisymmetric matrix.

    0 -4 9 0 3 -8
    A = 4 0 -6 , B = -3 0 7
    -9 6 0 8 -7 0

    0+0 -4+3 9+(-8)
    C = A + B = 4+(-3) 0+0 -6+7
    -9+8 6+(-7) 0+0

    0 -1 1
    = 1 0 1
    -1 -1 0

    0 1 -1
    Ct = -1 0 -1
    1 1 0

    0 -1 1
    -Ct = 1 0 1
    -1 -1 0

    C = -Ct (antisymmetric matrix)

  98. Nama : Pemula Budi Akbar
    NIM : 10.11.4536
    Kelas : S1-TI-1M

    1. Example of antisymmetric matrix:

    0 3 -2
    A = -3 0 1
    2 -1 0

    2. Prove that antisymmetric matrix is a square matrix with

    zero on each diagonal elements.
    Antisymmetric matrix is an anti of symmetric matrix, with (A= -At ). That mean the matrix is equal to its transpose, but each element of the transposed matrix has an opposite sign of the matrix.

    Here are two examples of symmetric matrix, one with zero on each diagonal elements.

    8 -4 9 0 -4 9
    A = 4 5 6 B = 4 0 6
    -9 -6 3 -9 -6 0

    8 4 -9 0 4 -9
    At = -4 5 -6 Bt = -4 0 -6
    9 6 3 9 6 0

    -8 -4 9 0 -4 9
    -At = 4 -5 6 -Bt = 4 0 6
    -9 -6 -3 -9 -6 0

    We could see that A != -At and B = -Bt. So it’s proved that antisymmetric matrix is a square matrix with zero on each diagonal elements.

    3. Prove that sum of two antisymmetric matrix is an

    antisymmetric matrix.

    0 -4 9 0 3 -8
    A = 4 0 -6 , B = -3 0 7
    -9 6 0 8 -7 0

    0+0 -4+3 9+(-8)
    C = A + B = 4+(-3) 0+0 -6+7
    -9+8 6+(-7) 0+0

    0 -1 1
    = 1 0 1
    -1 -1 0

    0 1 -1
    Ct = -1 0 -1
    1 1 0

    0 -1 1
    -Ct = 1 0 1
    -1 -1 0

    C = -Ct (antisymmetric matrix)

  99. Nama : senja permata dewanti
    NIM : 10.11.4511
    Kelas : S1-TI-1M

    1. Example of antisymmetric matrix:

    0 3 -2
    A = -3 0 1
    2 -1 0

    2. Prove that antisymmetric matrix is a square matrix with

    zero on each diagonal elements.
    Antisymmetric matrix is an anti of symmetric matrix, with (A= -At ). That mean the matrix is equal to its transpose, but each element of the transposed matrix has an opposite sign of the matrix.

    Here are two examples of symmetric matrix, one with zero on each diagonal elements.

    8 -4 9 0 -4 9
    A = 4 5 6 B = 4 0 6
    -9 -6 3 -9 -6 0

    8 4 -9 0 4 -9
    At = -4 5 -6 Bt = -4 0 -6
    9 6 3 9 6 0

    -8 -4 9 0 -4 9
    -At = 4 -5 6 -Bt = 4 0 6
    -9 -6 -3 -9 -6 0

    We could see that A != -At and B = -Bt. So it’s proved that antisymmetric matrix is a square matrix with zero on each diagonal elements.

    3. Prove that sum of two antisymmetric matrix is an

    antisymmetric matrix.

    0 -4 9 0 3 -8
    A = 4 0 -6 , B = -3 0 7
    -9 6 0 8 -7 0

    0+0 -4+3 9+(-8)
    C = A + B = 4+(-3) 0+0 -6+7
    -9+8 6+(-7) 0+0

    0 -1 1
    = 1 0 1
    -1 -1 0

    0 1 -1
    Ct = -1 0 -1
    1 1 0

    0 -1 1
    -Ct = 1 0 1
    -1 -1 0

    C = -Ct (antisymmetric matrix)

  100. Nama : Muhyiddin Al-Idrus
    NIM : 10.11.4540
    Kelas : 1M

    Pembuktian dengan menggunakan Matlab 7.10

    1. Example of antisymmetric matrix:

    >> A=[0 -2 -1;-2 0 3;1 -3 0]

    A =

    0 -2 -1
    -2 0 3
    1 -3 0

    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements:

    >> A=[6 -3 8;3 1 7;-8 -7 4],B=[0 -3 8;3 0 7;-8 -7 0]

    A =

    6 -3 8
    3 1 7
    -8 -7 4

    B =

    0 -3 8
    3 0 7
    -8 -7 0

    >> A’,B’

    ans =

    6 3 -8
    -3 1 -7
    8 7 4

    ans =

    0 3 -8
    -3 0 -7
    8 7 0

    >> -A’,-B’

    ans =

    -6 -3 8
    3 -1 7
    -8 -7 -4

    ans =

    0 -3 8
    3 0 7
    -8 -7 0

    Kita bisa melihat bahwa A =-At dan B =-Bt. Jadi itu membuktikan bahwa antisimetrik matriks adalah matriks persegi dengan nol pada setiap elemen diagonal.

    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.

    >> A=[0 -4 8;4 0 -5;-8 5 0],B=[0 7 -3;-7 0 6;3 -6 0]

    A =

    0 -4 8
    4 0 -5
    -8 5 0

    B =

    0 7 -3
    -7 0 6
    3 -6 0

    >> C=A+B

    C =

    0 3 5
    -3 0 1
    -5 -1 0

    >> C’

    ans =

    0 -3 -5
    3 0 -1
    5 1 0

    >> -C’

    ans =

    0 3 5
    -3 0 1
    -5 -1 0

    C = -Ct (antisymmetric matrix berarti bener)

  101. Nama : Muhyiddin Al-Idrus
    NIM : 10.11.4540
    Kelas : 1M

    1. Example of antisymmetric matrix:

    0 4 -3
    A = -4 0 6
    3 -6 0

    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements.

    6 -3 8 0 -2 7
    A = 3 1 7 B = 2 0 6
    8 -7 4 -7 -6 0

    6 3 -8 0 2 -7
    At = -3 1 -7 Bt = -2 0 -6
    8 7 4 7 6 0

    -6 -3 8 0 -2 7
    -At = 3 -1 7 -Bt = 2 0 6
    -8 -7 -4 -7 -6 0

    Kita bisa melihat bahwa A =-At dan B =-Bt. Jadi itu membuktikan bahwa antisimetrik matriks adalah matriks persegi dengan nol pada setiap elemen diagonal.

    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.

    0 -4 8 0 7 -3
    A = 4 0 -5 , B = -7 0 6
    -8 5 0 3 -6 0

    0+0 -4+7 8+(-3)
    C = A + B = 4+(-7) 0+0 -5+6
    -8+3 5+(-6) 0+0

    0 3 5
    = -3 0 1
    -5 -1 0

    0 -3 -5
    Ct = 3 0 -1
    5 1 0

    0 3 5
    -Ct = -3 0 1
    -5 -1 0

    C = -Ct (antisymmetric matrix)

  102. Nama : Soraya Inayah Fidran
    Kelas : S1 TI-M
    NIM : 10.11.4522

    1. Example of antisymmetric matrix:

    0 4 -2
    A = -3 2 5
    1 -5 0

    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements.

    Antisymmetric matrix is an anti of symmetric matrix, with (A= -At ). That mean the matrix is equal to its transpose, but each element of the transposed matrix has an opposite sign of the matrix.

    Here are two examples of symmetric matrix, one with zero on each diagonal elements.

    6 -2 1 6 5 9
    A = 4 2 5 B = -2 0 -1
    -8 -3 2 1 -4 2

    -6 2 1 -6 -5 -9
    At = -4 -2 -5 Bt = 2 0 1
    8 3 -2 -1 4 -2

    6 -2 1 6 5 9
    -At = 4 2 5 -Bt = -2 0 -1
    -8 -3 2 1 -4 2

    We could see that A != -At and B = -Bt. So it’s proved that antisymmetric matrix is a square matrix with zero on each diagonal elements.

    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.

    1 2 1 4 -2 -5
    Let A = 3 0 3 , B = -1 0 4
    -2 3 0 5 -4 0

    1+4 2+(-2) 1+(-5)
    C = A + B = 3+(-1) 0+0 3+4
    -2+5 3+(-4) 0+0

    5 0 -4
    = 2 0 7
    3 -1 0

    5 0 -4
    Ct = 2 0 7
    3 -1 0

    -5 0 4
    -Ct = -2 0 -7
    -3 1 0

    C = -Ct (antisymmetric matrix)

  103. Nama : Muhyiddin Al-Idrus
    Kelas : 1M

    1. Example of antisymmetric matrix:

    0 4 -3
    A = -4 0 6
    3 -6 0

    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements.

    6 -3 8 0 -2 7
    A = 3 1 7 B = 2 0 6
    -8 -7 4 -7 -6 0

    6 3 -8 0 2 -7
    At = -3 1 -7 Bt = -2 0 -6
    8 7 4 7 6 0

    -6 -3 8 0 -2 7
    -At = 3 -1 7 -Bt = 2 0 6
    -8 -7 -4 -7 -6 0

    Kita bisa melihat bahwa A =-At dan B =-Bt. Jadi itu membuktikan bahwa antisimetrik matriks adalah matriks persegi dengan nol pada setiap elemen diagonal.

    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.

    0 -4 8 0 7 -3
    A = 4 0 -5 , B = -7 0 6
    -8 5 0 3 -6 0

    0+0 -4+7 8+(-3)
    C = A + B = 4+(-7) 0+0 -5+6
    -8+3 5+(-6) 0+0

    0 3 5
    = -3 0 1
    -5 -1 0

    0 -3 -5
    Ct = 3 0 -1
    5 1 0

    0 3 5
    -Ct = -3 0 1
    -5 -1 0

    C = -Ct (antisymmetric matrix)

  104. Nama = Margubillah
    Nim = 09.11.3475
    Kelas = SITI – 3M

    Visual Basik

    Private Sub Command1_Click()
    If Text1.Text = “bill” Then
    Picture1.Visible = True
    Text1.Enabled = False
    Command1.Enabled = False
    Else
    MsgBox “password salah..”
    Text1.Text = “”
    End If
    End Sub

    ==========================================
    JAVA JDK

    public class Proposisi {
    public static void main(String args[])
    {
    String bill = “STMIK AMIKOM”; //Himpunan
    System.out.println(“Membaca banyak himpunan berupa huruf \n================================== “);
    System.out.println(“\nhimpunan x = \”” +bill +”\” size = “+bill.length()+ ” digit”);

    System.out.println(“Apakah himpunan dengan kata ‘STMIK’ = ” +bill.startsWith(“STMIK”));
    System.out.println(“Apakah himpunan dengan kata ‘AKAKOM’ = ” +bill.startsWith(“AKAKOM”));
    System.out.println(“Apakah himpunan dengan kata ‘AMIKOM’ = ” +bill.endsWith(“AMIKOM”));

    }

    }

  105. 1. Example of antisymmetric matrix:

    0 3 -2
    A = -3 0 5
    2 -5 0

    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements.

    Antisymmetric matrix is an anti of symmetric matrix, with (A= -At ). That mean the matrix is equal to its transpose, but each element of the transposed matrix has an opposite sign of the matrix.

    Here are two examples of symmetric matrix, one with zero on each diagonal elements.

    7 -4 9 0 -4 9
    A = 4 2 8 B = 4 0 8
    -9 -8 5 -9 -8 0

    7 4 -9 0 4 -9
    At = -4 2 -8 Bt = -4 0 -8
    9 8 5 9 8 0

    -7 -4 9 0 -4 9
    -At = 4 -2 8 -Bt = 4 0 8
    -9 -8 -5 -9 -8 0

    We could see that A != -At and B = -Bt. So it’s proved that antisymmetric matrix is a square matrix with zero on each diagonal elements.

    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.

    0 -3 7 0 11 -5
    Let A = 3 0 -4 , B = -11 0 8
    -7 4 0 5 -8 0

    0+0 -3+11 7+(-5)
    C = A + B = 3+(-11) 0+0 -4+8
    -7+5 4+(-8) 0+0

    0 8 2
    = -8 0 4
    -2 -4 0

    0 -8 -2
    Ct = 8 0 -4
    2 4 0

    0 8 2
    -Ct = -8 0 4
    -2 -4 0

    C = -Ct (antisymmetric matrix) –Proved–

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