sistem kontrol

SYSTEM KONTROL

NAMA : IKHWANI
NIM : 0708002010058
JURUSAN : D3 INSKOM
Soal 1

A=[10 4 6 12; 2 6 7 7; 3 5 4 6; 5 11 3 12]
A =

10 4 6 12
2 6 7 7
3 5 4 6
5 11 3 12
a) matriks ini bukan matriks singular karena nilai determinannya bukan nol (0) melainkan nilainya -294

b) determinan dari matrik A

det(A)
A=A'

ans =

-294
C) tranpose mtrik A

A =

11 13 15 16
17 18 17 12
13 15 16 18
12 18 19 13


d. invers matriks A
inv(A)
ans =

-0.0646 -0.6531 1.4490 -0.2789
-0.2007 -0.4490 1.1837 -0.1293
-0.0272 0.0408 0.3469 -0.1701
0.2177 0.6735 -1.7755 0.3605

e.hasil kali matrik A dengan tranpose
A*A'
138 122 101 212
122 198 119 252
101 119 110 181
212 252 181 373



Soal 2

A=[11 17 13 12 ; 13 18 15 18; 15 17 16 19 ; 16 12 18 13]
A =

11 17 13 12
13 18 15 18
15 17 16 19
16 12 18 13




B=[12 13 12 12; 15 17 13 14 ; 13 10 14 19; 15 19 13 16]
B =

12 13 12 12
15 17 13 14
13 10 14 19
15 19 13 16

A).determinan dari A dan B
det(A)
A =

11 13 15 16
17 18 17 12
13 15 16 18
12 18 19 13

det(B)
B =

12 15 13 15
13 17 10 19
12 13 14 13
12 14 19 16

b.invers A dan B

inv(A)

ans =

0.3778 -1.2133 1.0356 -0.1822
0.2148 -0.1644 0.0830 -0.0919
-0.3185 0.9956 -0.9437 0.2948
-0.2222 0.2667 -0.0444 -0.0222

inv(B)
ans =

-0.7195 1.0882 0.1041 -0.5362
0.1855 -0.3529 -0.1086 0.2986
0.7873 -0.5588 -0.0950 0.0113
-0.1855 -0.1471 0.1086 0.2014

c.tranpose dari matriks A dan B
A=A'
ans =

-675
B=B'
ans =

-442

d. nilai egen dan vektor eigen A dan B

[V,D]=eig(A)
V =
-0.4527 -0.4169 -0.1605i -0.4169 + 0.1605i -0.2712 -0.5233 0.4324 +0.5465i 0.4324 -0.5465i 0.5867
-0.5098 -0.3494 -0.2961i - 0.3494 +0.2961i -0.6692 -0.5113 0.3036 -0.1134i 0.3036 +0.1134i 0.3667


D =
60.9923 0 0 0 0 -0.6227 +2.4387i 0 0 0 0 -0.6227 - 2.4387i 0 0 0 0 -1.7470

[V,D]=eig(B)

V =

0.4842 -0.5771 -0.2600 + 0.0034i -0.2600 - 0.0034i
0.5245 0.7188 -0.3073 - 0.5915i -0.3073 + 0.5915i
0.4551 0.1505 -0.0796 + 0.3026i -0.0796 - 0.3026i
0.5323 -0.3572 0.5592 + 0.2783i 0.5592 - 0.2783i


D =

56.9569 0 0 0 -0.7870 0 0 0 0
1.415 + 2.8032i 0
0 0 0
1.4150 - 2.8032i 0


e. A X B

A*B

ans =

736 790 691 809
891 967 834 981
928 1005 872 1026
801 839 769 910

f. AT X BT

A=A'
A =

11 13 15 16
17 18 17 12
13 15 16 18
12 18 19 13

B=B'
B =

12 15 13 15
13 17 10 19
12 13 14 13
12 14 19 16


A'*B'
ans =

736 790 691 809
891 967 834 981
928 1005 872 1026
801 839 769 910