Jawaban quiz bagi kelas S1TI-1N
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Filed under: Linear Algebra and Matrices |
Reconfigurable Computing, Digital Signal Processing, Embedded Systems, System on Chip, and Algorithms 
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
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
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
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
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)
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)
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
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
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
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)
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
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)
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)
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
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
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
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)
>> 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
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
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
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
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
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
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
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)
###
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
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
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)
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
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)
######### 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