# Lab12 - A=[3 0 0 0 0-1 5 0 2-3 3 2 1-1-3 3[P,D]=eig(A...

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Exercise 1 A= [-1 -7 -3; -11 -12 -8; 16 41 20] [P,D]=eig(A) B1=P(:,1); B2=real(P(:,2)); B3=imag(P(:,2)); B= [B1 B2 B3] B denotes the coefficient matrix for the system w= [28; -82; -64] c=inv(B)*w G1=c(1)*B1; G2=c(2)*B2+c(3)*B3; G3=-c(2)*B3+c(3)*B2; G= [G1 G2 G3] This command simplifies the final answer by doing all the numerical multiplication and then adding coefficients of like terms. - - - - = t e t e e z y x t t t 6 sin 6 cos 676 37 27 242 91 9 112 19 9 3 3 The same process is used to solve the other problems, with slight variations to the placement of columns of P into B. Exercise 2 A= [15 -6 1; 56 -20 2; 17 -4 1] [P,D]=eig(A) B1=P(:,3); B2=real(P(:,1)); B3=imag(P(:,1)); B= [B1 B2 B3] w= [ 12; 38; 32] c=inv(B)*w G1=c(1)*B1; G2=c(2)*B2+c(3)*B3; G3=-c(2)*B3+c(3)*B2; G= [G1 G2 G3] - = - - t e t e e z y x t t t 5 sin 5 cos 6 2 30 0 20 18 2 6 6 3 3 2 Exercise 3

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Unformatted text preview: A= [3 0 0 0; 0 -1 5 0; 2 -3 3 2; 1 -1 -3 3] [P,D]=eig(A) B1=P(:,1); B2=P(:,4); B3=real(P(:,2)); B4=imag(P(:,2)); B= [B1 B2 B3 B4] -+ + + -+ -+ ---= 2390 . 3586 . 5979 . 4 sin 4781 . 4781 . 4 cos 4781 . 4781 . 4 sin 2390 . 3586 . 5976 . 4 cos 4634 . 1951 . 2439 . 8293 . 3 7145 . 2598 . 6496 . 2 4 2 3 2 1 t t e C t t e C t e C e C z y x t t t...
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Lab12 - A=[3 0 0 0 0-1 5 0 2-3 3 2 1-1-3 3[P,D]=eig(A...

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