Matlab HW 4 - Vaish Sridharan Section A04 Xuyu Zhang MATLAB...

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Vaish Sridharan Section A04 Xuyu Zhang MATLAB HW 4 Exercise 4.1 A. >> B = [1.2, 2.5; 4, 07.] B = 1.2000 2.5000 4.0000 7.0000 B. >> [eigvec, eigval] = eig(B) eigvec = -0.8739 -0.3284 0.4861 -0.9445 eigval = -0.1907 0 0 8.3907 Exercise 4.2 A. B. >> A = [1, 3; -1, -8] A = 1 3 -1 -8 >> [eigvec, eigval] = eig(A) eigvec = 0.9934 -0.3276 -0.1148 0.9448 eigval = 0.6533 0 0 -7.6533 C.
Vaish Sridharan Section A04 Xuyu Zhang D. Yes, the plot supports my answer to #C. Exercise 4.3 A. >> A = [2.7, -1; 4.1, 3.7] A = 2.7000 -1.0000 4.1000 3.7000 >> [eigvec, eigval] = eig(A) eigvec = -0.1093 + 0.4291i -0.1093 - 0.4291i 0.8966 + 0.0000i 0.8966 + 0.0000i eigval = 3.2000 + 1.9621i 0.0000 + 0.0000i 0.0000 + 0.0000i 3.2000 - 1.9621i B.
Vaish Sridharan Section A04 Xuyu Zhang C. The feature that causes the solutions to tend to infinity is the fact that the eigenvalues are positive, and so as t grows large, e is raised to a large positive number, which causes the solution to grow exponentially larger and tend to infinity. Exercise 4.4 A. >> A = [1.25, -0.97, 4.6; -2.6, -5.2, -0.31; 1.18, -10.3, 1.12] A = 1.2500 -0.9700 4.6000 -2.6000 -5.2000 -0.3100 1.1800 -10.3000 1.1200 >> [eigvec, eigval] = eig(A) eigvec = 0.7351 + 0.0000i -0.4490 - 0.2591i -0.4490 + 0.2591i -0.1961 + 0.0000i 0.3375 - 0.2242i 0.3375 + 0.2242i 0.6490 + 0.0000i 0.7530 + 0.0000i 0.7530 + 0.0000i eigval = 5.5698 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i -4.1999 + 2.6606i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i -4.1999 - 2.6606i B. The system is not stable, because the first eigenvalue is positive but the second and third eigenvalues are negative.
Vaish Sridharan

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