Jawaban quiz bagi kelas S1TI-1N

Jawaban quiz bagi kelas S1TI-1N

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  2. Jangan lupa menuliskan nama dan NIM anda.
  3. Ingat perhatikan baik-baik kelas anda.

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31 Responses

  1. Nama : Joko Prasetyo
    NIM : 10.11.4597
    Kelas : S1 TI N

    Jawaban soal A

    >> X=[ 0 2 -9 4 ; -2 0 -7 3 ; 9 7 0 -1 ; -4 -3 1 0 ]
    X =
    0 2 -9 4
    -2 0 -7 3
    9 7 0 -1
    -4 -3 1 0
    >> -X’
    ans =
    0 2 -9 4
    -2 0 -7 3
    9 7 0 -1
    -4 -3 1 0

    Jawaban soal B

    >> A=[0 -3 -5; 3 0 3 ; 5 -3 0]
    A =
    0 -3 -5
    3 0 3
    5 -3 0
    >> -A’
    ans =
    0 -3 -5
    3 0 3
    5 -3 0

    Jawaban soal C

    >> M=[ 0 7 -8 ; -7 0 -1 ; 8 1 0]
    M =
    0 7 -8
    -7 0 -1
    8 1 0
    >> -M’
    ans =
    0 7 -8
    -7 0 -1
    8 1 0
    >> N=[ 0 -3 9 ; 3 0 -4 ; -9 4 0]
    N =
    0 -3 9
    3 0 -4
    -9 4 0
    >> -N’
    ans =
    0 -3 9
    3 0 -4
    -9 4 0
    >> M+N
    ans =
    0 4 1
    -4 0 -5
    -1 5 0
    >> -(M+N)’
    ans =
    0 4 1
    -4 0 -5
    -1 5 0

  2. Jawaban soal A

    >> X=[ 0 2 -9 4 ; -2 0 -7 3 ; 9 7 0 -1 ; -4 -3 1 0 ]
    X =
    0 2 -9 4
    -2 0 -7 3
    9 7 0 -1
    -4 -3 1 0
    >> -X’
    ans =
    0 2 -9 4
    -2 0 -7 3
    9 7 0 -1
    -4 -3 1 0

    Jawaban soal B

    >> A=[0 -3 -5; 3 0 3 ; 5 -3 0]
    A =
    0 -3 -5
    3 0 3
    5 -3 0
    >> -A’
    ans =
    0 -3 -5
    3 0 3
    5 -3 0

    Jawaban soal C

    >> M=[ 0 7 -8 ; -7 0 -1 ; 8 1 0]
    M =
    0 7 -8
    -7 0 -1
    8 1 0
    >> -M’
    ans =
    0 7 -8
    -7 0 -1
    8 1 0
    >> N=[ 0 -3 9 ; 3 0 -4 ; -9 4 0]
    N =
    0 -3 9
    3 0 -4
    -9 4 0
    >> -N’
    ans =
    0 -3 9
    3 0 -4
    -9 4 0
    >> M+N
    ans =
    0 4 1
    -4 0 -5
    -1 5 0
    >> -(M+N)’
    ans =
    0 4 1
    -4 0 -5
    -1 5 0

  3. Nama : Joko Prasetyo
    NIM : 10.11.4597
    Kelas : S1 TI N

    Jawaban soal A

    >> X=[ 0 2 -9 4 ; -2 0 -7 3 ; 9 7 0 -1 ; -4 -3 1 0 ]
    X =
    0 2 -9 4
    -2 0 -7 3
    9 7 0 -1
    -4 -3 1 0
    >> -X’
    ans =
    0 2 -9 4
    -2 0 -7 3
    9 7 0 -1
    -4 -3 1 0

    Jawaban soal B

    >> A=[0 -3 -5; 3 0 3 ; 5 -3 0]
    A =
    0 -3 -5
    3 0 3
    5 -3 0
    >> -A’
    ans =
    0 -3 -5
    3 0 3
    5 -3 0

    Jawaban soal C

    >> M=[ 0 7 -8 ; -7 0 -1 ; 8 1 0]
    M =
    0 7 -8
    -7 0 -1
    8 1 0
    >> -M’
    ans =
    0 7 -8
    -7 0 -1
    8 1 0
    >> N=[ 0 -3 9 ; 3 0 -4 ; -9 4 0]
    N =
    0 -3 9
    3 0 -4
    -9 4 0
    >> -N’
    ans =
    0 -3 9
    3 0 -4
    -9 4 0
    >> M+N
    ans =
    0 4 1
    -4 0 -5
    -1 5 0
    >> -(M+N)’
    ans =
    0 4 1
    -4 0 -5
    -1 5 0

  4. Nama : Muh Rais Ulil Albab
    NIM : 10.11.4586
    Kelas : S1 TI N

    —–soal A—–

    >> X=[ 0 2 -9 4 ; -2 0 -7 3 ; 9 7 0 -1 ; -4 -3 1 0 ]
    X =
    0 2 -9 4
    -2 0 -7 3
    9 7 0 -1
    -4 -3 1 0
    >> -X’
    ans =
    0 2 -9 4
    -2 0 -7 3
    9 7 0 -1
    -4 -3 1 0

    ——Soal B—–

    >> A=[0 -3 -5; 3 0 3 ; 5 -3 0]
    A =
    0 -3 -5
    3 0 3
    5 -3 0
    >> -A’
    ans =
    0 -3 -5
    3 0 3
    5 -3 0

    ——SOAL C——

    >> M=[ 0 7 -8 ; -7 0 -1 ; 8 1 0]
    M =
    0 7 -8
    -7 0 -1
    8 1 0
    >> -M’
    ans =
    0 7 -8
    -7 0 -1
    8 1 0
    >> N=[ 0 -3 9 ; 3 0 -4 ; -9 4 0]
    N =
    0 -3 9
    3 0 -4
    -9 4 0
    >> -N’
    ans =
    0 -3 9
    3 0 -4
    -9 4 0
    >> M+N
    ans =
    0 4 1
    -4 0 -5
    -1 5 0
    >> -(M+N)’
    ans =
    0 4 1
    -4 0 -5
    -1 5 0

  5. Nama : Yuda Hadi Prayoko
    Kelas : S1-TI-1N
    NIM : 10.11.4594

    Nama : Aloisius Chris Cahyo Utomo
    NIM : 10.11.4563
    Kelas : S1-TI-1N

    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)

  6. Nama : Aloisius Chris Cahyo Utomo
    NIM : 10.11.4563
    Kelas : S1-TI-1N

    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)

  7. Nama : Septifani Madianingrum
    NIM : 10.11.4551
    Kelas : S1-TI-N
    1. Example of antisymmetric matrix:

    >> A = [0,2,-4;-2,0,5;4,-5,0]
    A =
    0 2 -4
    -2 0 5
    4 -5 0

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

    0-3 8 0 -2 7
    A = 3 0 7 B = 2 0 6
    -8 -7 0 -7 -6 0
    0 3 -8 0 2 -7
    At = -3 0 -7 Bt = -2 0 -6
    8 7 0 7 6 0
    0 -3 8 0 -2 7
    -At = 3 0 7 -Bt = 2 0 6
    -8 -7 0 -7 -6 0
    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.

    >> A = [0,1,2;-1,0,4;-2,-4,0]
    A =
    0 1 2
    -1 0 4
    -2 -4 0
    >> -A’
    ans =
    0 1 2
    -1 0 4
    -2 -4 0
    >> B = [0,4,6;-4,0,3;-6,-3,0]
    B =
    0 4 6
    -4 0 3
    -6 -3 0
    >> -B’
    ans =
    0 4 6
    -4 0 3
    -6 -3 0
    >> C = A+B
    C =
    0 5 8
    -5 0 7
    -8 -7 0
    >> -C’
    ans =
    0 5 8
    -5 0 7
    -8 -7 0
    >> C=-C’
    C =
    0 5 8
    -5 0 7
    -8 -7 0

  8. Nama : R A Atika Diah Sitawati
    NIM : 10.11.4566
    Kelas : S1-TI-N
    1. Example of antisymmetric matrix:

    >> A = [0,2,-4;-2,0,5;4,-5,0]
    A =
    0 2 -4
    -2 0 5
    4 -5 0

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

    0-3 8 0 -2 7
    A = 3 0 7 B = 2 0 6
    -8 -7 0 -7 -6 0
    0 3 -8 0 2 -7
    At = -3 0 -7 Bt = -2 0 -6
    8 7 0 7 6 0
    0 -3 8 0 -2 7
    -At = 3 0 7 -Bt = 2 0 6
    -8 -7 0 -7 -6 0
    3. Prove that sum of two antisymmetric matrix is an antisymmetric matrix.

    >> A = [0,1,2;-1,0,4;-2,-4,0]
    A =
    0 1 2
    -1 0 4
    -2 -4 0
    >> -A’
    ans =
    0 1 2
    -1 0 4
    -2 -4 0
    >> B = [0,4,6;-4,0,3;-6,-3,0]
    B =
    0 4 6
    -4 0 3
    -6 -3 0
    >> -B’
    ans =
    0 4 6
    -4 0 3
    -6 -3 0
    >> C = A+B
    C =
    0 5 8
    -5 0 7
    -8 -7 0
    >> -C’
    ans =
    0 5 8
    -5 0 7
    -8 -7 0
    >> C=-C’
    C =
    0 5 8
    -5 0 7
    -8 -7 0

  9. Nama : Fikria Rifdania R
    NIM : 10.11.4591
    Kelas : S1-TI-N
    1. Example of antisymmetric matrix:

    >> A = [0,2,-4;-2,0,5;4,-5,0]
    A =
    0 2 -4
    -2 0 5
    4 -5 0

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

    0-3 8 0 -2 7
    A = 3 0 7 B = 2 0 6
    -8 -7 0 -7 -6 0
    0 3 -8 0 2 -7
    At = -3 0 -7 Bt = -2 0 -6
    8 7 0 7 6 0
    0 -3 8 0 -2 7
    -At = 3 0 7 -Bt = 2 0 6
    -8 -7 0 -7 -6 0

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

    >> A = [0,1,2;-1,0,4;-2,-4,0]
    A =
    0 1 2
    -1 0 4
    -2 -4 0
    >> -A’
    ans =
    0 1 2
    -1 0 4
    -2 -4 0

    >> B = [0,4,6;-4,0,3;-6,-3,0]
    B =
    0 4 6
    -4 0 3
    -6 -3 0
    >> -B’
    ans =
    0 4 6
    -4 0 3
    -6 -3 0

    >> C = A+B
    C =
    0 5 8
    -5 0 7
    -8 -7 0
    >> -C’
    ans =
    0 5 8
    -5 0 7
    -8 -7 0
    >> C=-C’
    C =
    0 5 8
    -5 0 7
    -8 -7 0

  10. irwan rudianto anugrah
    10.11.4605

    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)

  11. 1. Example of antisymmetric matrix:
    >> A = [0,2,-4;-2,0,5;4,-5,0]

    A =

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

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

    A =

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

    >> -A’

    ans =

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

    >> B = [0,4,6;-4,0,3;-6,-3,0]

    B =

    0 4 6
    -4 0 3
    -6 -3 0

    >> -B’

    ans =

    0 4 6
    -4 0 3
    -6 -3 0

    >> C = A+B

    C =

    0 5 8
    -5 0 7
    -8 -7 0

    >> -C’

    ans =

    0 5 8
    -5 0 7
    -8 -7 0

    >> C=-C’

    C =

    0 5 8
    -5 0 7
    -8 -7 0

  12. Joko Tri Purwanto
    10.11.4561

    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)

  13. NAMA : FENDY SAPTO PURWOKO
    NIM : 10.11.4580
    JURUSAN : S1 TI-1N

    ================Soal A================
    >> A=[ 0 2 4 ; -2 0 6 ; -4 -6 0 ]

    A =
    0 2 4
    -2 0 6
    -4 -6 0
    >> -A’

    ans =
    0 2 4
    -2 0 6
    -4 -6 0

    FENDY SAPTO PURWOKO
    ================Soal B================
    >> B=[0 1 2; -1 0 3 ; -2 -3 0]
    B =
    0 1 2
    -1 0 3
    -2 -3 0
    >> -B’
    ans =
    0 1 2
    -1 0 3
    -2 -3 0
    (Matriks persegi dan mempunyai diagonal nol)

    FENDY SAPTO PURWOKO
    ================Soal C================
    >> A+B
    ans =
    0 3 6
    -3 0 9
    -6 -9 0
    >> -(A+B)’
    ans =
    0 3 6
    -3 0 9
    -6 -9 0
    (Jumlah dua matriks antisymmetric adalah matriks antisymmetric juga)

  14. Nama : Katty Rossyanna
    NIM : 10.11.4599
    Kelas : S1 TI_1N
    JAWABAN SOAL A

    >> A=[ 0 3 -7 4 ; -3 0 -7 3 ; 7 7 0 -1 ; -4 -3 1 0 ]
    A =
    0 3 -7 4
    -3 0 -7 3
    …… 7 7 0 -1
    -4 -3 1 0
    >> -A’
    ans =
    0 3 -7 4
    -3 0 -7 3
    7 7 0 -1
    -4 -3 1 0

    JAWABAN SOAL B
    >> B=[0 -1 3; 1 0 2 ; -3 -2 0]
    B =
    0 -1 3
    1 0 2
    -3 -2 0
    >> -B’
    ans =
    0 -1 3
    1 0 2
    -3 -2 0

    JAWABAN SOAL C
    >> C=[ 0 4 -5 ; -4 0 -7 ; 5 7 0]
    C =
    0 4 -5
    -4 0 -7
    5 7 0
    >> -C’
    ans =
    0 4 -5
    -4 0 -7
    5 7 0
    >> D=[ 0 9 -2 ; -9 0 -4 ; 2 4 0]
    D =
    0 9 -2
    -9 0 -4
    2 4 0
    >> -D’
    ans =
    0 9 -2
    -9 0 -4
    2 4 0
    >> C+D
    ans =
    0 13 -7
    -13 0 -11
    7 11 0
    >> -(C+D)’
    ans =
    0 13 -7
    -13 0 -11
    7 11 0

  15. NAMA = DIRGANA
    NIM =4559
    KELAS =S1 TI

    1. Example of antisymmetric matrix:
    >> A = [0,2,-4;-2,0,5;4,-5,0]

    A =

    0 2 -4
    -2 0 5
    4 -5 0
    2. Prove that antisymmetric matrix is a square matrix with zero on each diagonal elements.

    >> A = [0,1,2;-1,0,4;-2,-4,0]

    A =

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

    >> -A’

    ans =

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

    >> B = [0,4,6;-4,0,3;-6,-3,0]

    B =

    0 4 6
    -4 0 3
    -6 -3 0

    >> -B’

    ans =

    0 4 6
    -4 0 3
    -6 -3 0

    >> C = A+B

    C =

    0 5 8
    -5 0 7
    -8 -7 0

    >> -C’

    ans =

    0 5 8
    -5 0 7
    -8 -7 0

    >> C=-C’

    C =

    0 5 8
    -5 0 7
    -8 -7 0

  16. NAMA = RELLY PUSPITA
    NIM =4587
    KELAS =S1 TI

    1. Example of antisymmetric matrix:
    >> A = [0,2,-4;-2,0,5;4,-5,0]

    A =

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

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

    A =

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

    >> -A’

    ans =

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

    >> B = [0,4,6;-4,0,3;-6,-3,0]

    B =

    0 4 6
    -4 0 3
    -6 -3 0

    >> -B’

    ans =

    0 4 6
    -4 0 3
    -6 -3 0

    >> C = A+B

    C =

    0 5 8
    -5 0 7
    -8 -7 0

    >> -C’

    ans =

    0 5 8
    -5 0 7
    -8 -7 0

    >> C=-C’

    C =

    0 5 8
    -5 0 7
    -8 -7 0

  17. 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)

  18. >> A=[ 0 4 -8 5 ; -4 0 -8 4 ; 8 8 0 -2 ; -5 -4 2 0 ]

    A =

    0 4 -8 5
    -4 0 -8 4
    8 8 0 -2
    -5 -4 2 0

    >> -A’

    ans =

    0 4 -8 5
    -4 0 -8 4
    8 8 0 -2
    -5 -4 2 0

    >> B=[0 -3 5; 3 0 4 ; -5 -4 0]

    B =

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

    >> -B’

    ans =

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

    >> C=[ 0 7 -8; -7 0 -9 ; 8 9 0]

    C =

    0 7 -8
    -7 0 -9
    8 9 0

    >> -C’

    ans =

    0 7 -8
    -7 0 -9
    8 9 0

    >> D=[ 0 7 -4 ; -7 0 -3 ; 4 3 0]

    D =

    0 7 -4
    -7 0 -3
    4 3 0

    >> -D’

    ans =

    0 7 -4
    -7 0 -3
    4 3 0

    >> C+D

    ans =

    0 14 -12
    -14 0 -12
    12 12 0

    >> -(C+D)’

    ans =

    0 14 -12
    -14 0 -12
    12 12 0

  19. JAWABAN SOAL A
    >>
    A=[ 0 3 -7 4 ; -3 0 -7 3 ; 7 7 0 -1 ; -4 -3 1 0 ]

    A =
    … 0 3 -7 4
    -3 0 -7 3
    7 7 0 -1
    -4 -3 1 0
    >>
    -A’

    ans =
    0 3 -7 4
    -3 0 -7 3
    7 7 0 -1
    -4 -3 1 0
    JAWABAN SOAL B
    >> B=[0 -1 3; 1 0 2 ; -3 -2 0]
    B =
    0 -1 3
    1 0 2
    -3 -2 0
    >> -B’
    ans =
    0 -1 3
    1 0 2
    -3 -2 0
    JAWABAN SOAL C
    >> C=[ 0 4 -5 ; -4 0 -7 ; 5 7 0]
    C =
    0 4 -5
    -4 0 -7
    5 7 0
    >> -C’
    ans =
    0 4 -5
    -4 0 -7
    5 7 0
    >> D=[ 0 9 -2 ; -9 0 -4 ; 2 4 0]
    D =
    0 9 -2
    -9 0 -4
    2 4 0
    >> -D’
    ans =
    0 9 -2
    -9 0 -4
    2 4 0
    >> C+D
    ans =
    0 13 -7
    -13 0 -11
    7 11 0
    >> -(C+D)’
    ans =
    0 13 -7
    -13 0 -11
    7 11 0

  20. Alif Aziz
    10.11.4615

    ######### JAWABAN SOAL A ##########

    >> X=[ 0 2 -9 4 ; -2 0 -7 3 ; 9 7 0 -1 ; -4 -3 1 0 ]
    X =
    0 2 -9 4
    -2 0 -7 3
    9 7 0 -1
    -4 -3 1 0

    >> -X’
    ans =
    0 2 -9 4
    -2 0 -7 3
    9 7 0 -1
    -4 -3 1 0

    ######### JAWABAN SOAL B ##########

    >> A=[0 -3 -5; 3 0 3 ; 5 -3 0]
    A =
    0 -3 -5
    3 0 3
    5 -3 0

    >> -A’
    ans =
    0 -3 -5
    3 0 3
    5 -3 0

    ######### JAWABAN SOAL C ##########

    >> M=[ 0 7 -8 ; -7 0 -1 ; 8 1 0]
    M =
    0 7 -8
    -7 0 -1
    8 1 0

    >> -M’
    ans =
    0 7 -8
    -7 0 -1
    8 1 0

    >> N=[ 0 -3 9 ; 3 0 -4 ; -9 4 0]
    N =
    0 -3 9
    3 0 -4
    -9 4 0

    >> -N’
    ans =
    0 -3 9
    3 0 -4
    -9 4 0

    >> M+N
    ans =
    0 4 1
    -4 0 -5
    -1 5 0

    >> -(M+N)’
    ans =
    0 4 1
    -4 0 -5
    -1 5 0

  21. Agung Okta Fiyanto
    10.11.4608

    JAWABAN SOAL A
    >> A=[ 0 3 -7 4 ; -3 0 -7 3 ; 7 7 0 -1 ; -4 -3 1 0 ]
    A =
    0 3 -7 4
    -3 0 -7 3
    …… 7 7 0 -1
    -4 -3 1 0
    >> -A’
    ans =
    0 3 -7 4
    -3 0 -7 3
    7 7 0 -1
    -4 -3 1 0
    JAWABAN SOAL B
    >> B=[0 -1 3; 1 0 2 ; -3 -2 0]
    B =
    0 -1 3
    1 0 2
    -3 -2 0
    >> -B’
    ans =
    0 -1 3
    1 0 2
    -3 -2 0
    JAWABAN SOAL C
    >> C=[ 0 4 -5 ; -4 0 -7 ; 5 7 0]
    C =
    0 4 -5
    -4 0 -7
    5 7 0
    >> -C’
    ans =
    0 4 -5
    -4 0 -7
    5 7 0
    >> D=[ 0 9 -2 ; -9 0 -4 ; 2 4 0]
    D =
    0 9 -2
    -9 0 -4
    2 4 0
    >> -D’
    ans =
    0 9 -2
    -9 0 -4
    2 4 0
    >> C+D
    ans =
    0 13 -7
    -13 0 -11
    7 11 0
    >> -(C+D)’
    ans =
    0 13 -7
    -13 0 -11
    7 11 0

  22. Jeffri Ardiansyah
    10.11.4570

    SOAL A
    >> A=[ 0 3 -7 4 ; -3 0 -7 3 ; 7 7 0 -1 ; -4 -3 1 0 ]
    A =
    0 3 -7 4
    -3 0 -7 3
    …… 7 7 0 -1
    -4 -3 1 0
    >> -A’
    ans =
    0 3 -7 4
    -3 0 -7 3
    7 7 0 -1
    -4 -3 1 0

    SOAL B
    >> B=[0 -1 3; 1 0 2 ; -3 -2 0]
    B =
    0 -1 3
    1 0 2
    -3 -2 0
    >> -B’
    ans =
    0 -1 3
    1 0 2
    -3 -2 0

    SOAL C
    >> C=[ 0 4 -5 ; -4 0 -7 ; 5 7 0]
    C =
    0 4 -5
    -4 0 -7
    5 7 0
    >> -C’
    ans =
    0 4 -5
    -4 0 -7
    5 7 0
    >> D=[ 0 9 -2 ; -9 0 -4 ; 2 4 0]
    D =
    0 9 -2
    -9 0 -4
    2 4 0
    >> -D’
    ans =
    0 9 -2
    -9 0 -4
    2 4 0
    >> C+D
    ans =
    0 13 -7
    -13 0 -11
    7 11 0
    >> -(C+D)’
    ans =
    0 13 -7
    -13 0 -11
    7 11 0

  23. SOAL A
    >> A=[ 0 3 -7 4 ; -3 0 -7 3 ; 7 7 0 -1 ; -4 -3 1 0 ]
    A =
    0 3 -7 4
    -3 0 -7 3
    …… 7 7 0 -1
    -4 -3 1 0
    >> -A’
    ans =
    0 3 -7 4
    -3 0 -7 3
    7 7 0 -1
    -4 -3 1 0

    SOAL B
    >> B=[0 -1 3; 1 0 2 ; -3 -2 0]
    B =
    0 -1 3
    1 0 2
    -3 -2 0
    >> -B’
    ans =
    0 -1 3
    1 0 2
    -3 -2 0

    SOAL C
    >> C=[ 0 4 -5 ; -4 0 -7 ; 5 7 0]
    C =
    0 4 -5
    -4 0 -7
    5 7 0
    >> -C’
    ans =
    0 4 -5
    -4 0 -7
    5 7 0
    >> D=[ 0 9 -2 ; -9 0 -4 ; 2 4 0]
    D =
    0 9 -2
    -9 0 -4
    2 4 0
    >> -D’
    ans =
    0 9 -2
    -9 0 -4
    2 4 0
    >> C+D
    ans =
    0 13 -7
    -13 0 -11
    7 11 0
    >> -(C+D)’
    ans =
    0 13 -7
    -13 0 -11
    7 11 0

  24. erwan (10.11.4564)
    JAWABAN SOAL A
    >>
    A=[ 0 3 -7 4 ; -3 0 -7 3 ; 7 7 0 -1 ; -4 -3 1 0 ]

    A =
    … 0 3 -7 4
    -3 0 -7 3
    7 7 0 -1
    -4 -3 1 0
    >>
    -A’

    ans =
    0 3 -7 4
    -3 0 -7 3
    7 7 0 -1
    -4 -3 1 0
    JAWABAN SOAL B
    >> B=[0 -1 3; 1 0 2 ; -3 -2 0]
    B =
    0 -1 3
    1 0 2
    -3 -2 0
    >> -B’
    ans =
    0 -1 3
    1 0 2
    -3 -2 0
    JAWABAN SOAL C
    >> C=[ 0 4 -5 ; -4 0 -7 ; 5 7 0]
    C =
    0 4 -5
    -4 0 -7
    5 7 0
    >> -C’
    ans =
    0 4 -5
    -4 0 -7
    5 7 0
    >> D=[ 0 9 -2 ; -9 0 -4 ; 2 4 0]
    D =
    0 9 -2
    -9 0 -4
    2 4 0
    >> -D’
    ans =
    0 9 -2
    -9 0 -4
    2 4 0
    >> C+D
    ans =
    0 13 -7
    -13 0 -11
    7 11 0
    >> -(C+D)’
    ans =
    0 13 -7
    -13 0 -11
    7 11 0

  25. HAPPY ALFI AZIZAH
    10.11.4585
    S1TI-1N
    A matrix A is said to be antisymmetric if A=-At

    1. Give an 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 an antisymmetric matrix is a square matrix having diagonal elements zero :

    >> 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

    Dapat kita lihat bahwa A =-At dan B =-Bt.
    Hal tersebut membuktikan bahwa antisimetrik matriks adalah matriks persegi yang elemen diagonalnya adalah nol.

    3. Prove that the sum of two antisymmetric matrices of the same size 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. JAWABAN SOAL A
    >> A=[ 0 3 -7 4 ; -3 0 -7 3 ; 7 7 0 -1 ; -4 -3 1 0 ]

    A =

    0 3 -7 4
    -3 0 -7 3
    7 7 0 -1
    -4 -3 1 0

    >> -A’

    ans =

    0 3 -7 4
    -3 0 -7 3
    7 7 0 -1
    -4 -3 1 0

    JAWABAN SOAL B
    >> B=[0 -1 3; 1 0 2 ; -3 -2 0]

    B =

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

    >> -B’

    ans =

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

    JAWABAN SOAL C
    >> C=[ 0 4 -5 ; -4 0 -7 ; 5 7 0]

    C =

    0 4 -5
    -4 0 -7
    5 7 0

    >> -C’

    ans =

    0 4 -5
    -4 0 -7
    5 7 0

    >> D=[ 0 9 -2 ; -9 0 -4 ; 2 4 0]

    D =

    0 9 -2
    -9 0 -4
    2 4 0

    >> -D’

    ans =

    0 9 -2
    -9 0 -4
    2 4 0

    >> C+D

    ans =

    0 13 -7
    -13 0 -11
    7 11 0

    >> -(C+D)’

    ans =

    0 13 -7
    -13 0 -11
    7 11 0

  27. NAMA : RIAN ADI WIBOWO
    NIM : 10.11.4546
    KELAS : S1-TI N

    ANTISYMMETRICMATRIX

    a matrix is said to be antisymmetric if A = -At

    a) >> x = [0 3 5; -3 0 8; -5 -8 0]
    x =
    0 3 5
    -3 0 8
    -5 -8 0
    >> -x’
    ans =
    0 3 5
    -3 0 8
    -5 -8 0

    b) >> y = [0 8 -1; -8 0 7; 1 -7 0]
    y =
    0 8 -1
    -8 0 7
    1 -7 0

    >> -y’
    ans =
    0 8 -1
    -8 0 7
    1 -7 0

    c) >> A = [0 5 3 -7; -5 0 -8 4; -3 8 0 6; 7 -4 -6 0]
    A =
    0 5 3 -7
    -5 0 -8 4
    -3 8 0 6
    7 -4 -6 0
    >> -A’
    ans =
    0 5 3 -7
    -5 0 -8 4
    -3 8 0 6
    7 -4 -6 0

    >> B = [0 -2 -6 -1; 2 0 5 -8; 6 -5 0 3; 1 8 -3 0]
    B =
    0 -2 -6 -1
    2 0 5 -8
    6 -5 0 3
    1 8 -3 0

    >> -B’
    ans =
    0 -2 -6 -1
    2 0 5 -8
    6 -5 0 3
    1 8 -3 0

    >> A + B
    ans =
    0 3 -3 -8
    -3 0 -3 -4
    3 3 0 9
    8 4 -9 0

    >> -A’ + -B’
    ans =
    0 3 -3 -8
    -3 0 -3 -4
    3 3 0 9
    8 4 -9 0

  28. Nama : Wegig Yoga Yunanta
    NIM : 10.11.4607
    Kelas : S1 – TI 1N

    1.Give an example of an antisymmetric matrix !
    Example:
    .>> A = [0 7 -1; -7 0 9; 1 -9 0]

    A =

    0 7 -1
    -7 0 9
    1 -9 0
    2.Prove that an antisymmetric matrix is a squer matrix having diagonal elements zero!
    .::Proof ::.
    >> A

    A =[2 -5 9; 5 1 1; -9 -1 3]

    2 -5 9
    5 1 1
    -9 -1 3

    >> B=[0 -5 9; 5 0 1; -9 -1 0]

    B =

    0 -5 9
    5 0 1
    -9 -1 0

    >> A’

    ans =

    2 5 -9
    -5 1 -1
    9 1 3

    >> B’

    ans =

    0 5 -9
    -5 0 -1
    9 1 0

    >> -A’

    ans =

    -2 -5 9
    5 -1 1
    -9 -1 -3

    >> -B’

    ans =

    0 -5 9
    5 0 1
    -9 -1 0

    A != -A’ and B = -B’

    3.Prove that the sum of two antisymmetric matrix matrices of the same size is an antisymmetric matrix!
    .::Proof ::.
    >> A = [0 6 -2; -6 0 9; 2 -9 0]

    A =

    0 6 -2
    -6 0 9
    2 -9 0

    >> B = [0 -4 1; 4 0 -5; -1 5 0]

    B =

    0 -4 1
    4 0 -5
    -1 5 0

    >> C = A + B

    C =

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

    >> C’

    ans =

    0 -2 1
    2 0 -4
    -1 4 0
    >> -C’

    ans =

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

  29. a.
    >> X=[ 0 2 -9 4 ; -2 0 -7 3 ; 9 7 0 -1 ; -4 -3 1 0 ]
    X =
    0 2 -9 4
    -2 0 -7 3
    9 7 0 -1
    -4 -3 1 0

    >> -X’
    ans =
    0 2 -9 4
    -2 0 -7 3
    9 7 0 -1
    -4 -3 1 0

    b.
    >> A=[0 -3 -5; 3 0 3 ; 5 -3 0]
    A =
    0 -3 -5
    3 0 3
    5 -3 0

    >> -A’
    ans =
    0 -3 -5
    3 0 3
    5 -3 0

    c.
    >> M=[ 0 7 -8 ; -7 0 -1 ; 8 1 0]
    M =
    0 7 -8
    -7 0 -1
    8 1 0

    >> -M’
    ans =
    0 7 -8
    -7 0 -1
    8 1 0

    >> N=[ 0 -3 9 ; 3 0 -4 ; -9 4 0]
    N =
    0 -3 9
    3 0 -4
    -9 4 0

    >> -N’
    ans =
    0 -3 9
    3 0 -4
    -9 4 0

    >> M+N
    ans =
    0 4 1
    -4 0 -5
    -1 5 0

    >> -(M+N)’
    ans =
    0 4 1
    -4 0 -5
    -1 5 0

  30. NAMA : NINDA KHANA AINURROKHISA
    NIM : 10.11.4577

    1. An example of an antisymetric matrix below :

    0 6 4
    -2 0 8
    -3 2 0
    2. An antisymmetric matrix is a square matrix that satisfies the identity

    where is the matrix transpose. For example,

    is antisymmetric. Antisymmetric matrices are commonly called “skew symmetric matrices” by mathematicians.
    A matrix may be tested to see if it is antisymmetric using the Mathematica function
    AntisymmetricQ[m_List?MatrixQ] :=
    (m === -Transpose[m])
    In component notation, this becomes

    Letting , the requirement becomes

    SO, AN ANTISYMETRIC MATRIX MUST HAVE ZEROS ON IT’S DIAGONAL.
    The general antisymmetric matrix is of the form

    0 a12 a 13

    -a12 0 a23

    -a13 a23 0

    (PROVED)

    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

    (PROVED)

  31. ######### JAWABAN SOAL A ##########

    >> X=[ 0 2 -9 4 ; -2 0 -7 3 ; 9 7 0 -1 ; -4 -3 1 0 ]
    X =
    0 2 -9 4
    -2 0 -7 3
    9 7 0 -1
    -4 -3 1 0

    >> -X’
    ans =
    0 2 -9 4
    -2 0 -7 3
    9 7 0 -1
    -4 -3 1 0

    ######### JAWABAN SOAL B ##########

    >> A=[0 -3 -5; 3 0 3 ; 5 -3 0]
    A =
    0 -3 -5
    3 0 3
    5 -3 0

    >> -A’
    ans =
    0 -3 -5
    3 0 3
    5 -3 0

    ######### JAWABAN SOAL C ##########

    >> M=[ 0 7 -8 ; -7 0 -1 ; 8 1 0]
    M =
    0 7 -8
    -7 0 -1
    8 1 0

    >> -M’
    ans =
    0 7 -8
    -7 0 -1
    8 1 0

    >> N=[ 0 -3 9 ; 3 0 -4 ; -9 4 0]
    N =
    0 -3 9
    3 0 -4
    -9 4 0

    >> -N’
    ans =
    0 -3 9
    3 0 -4
    -9 4 0

    >> M+N
    ans =
    0 4 1
    -4 0 -5
    -1 5 0

    >> -(M+N)’
    ans =
    0 4 1
    -4 0 -5
    -1 5 0

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