Assignment4 - Xiaoxin Xu Math20D matlab#4 A91068067 Chris...

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Xiaoxin Xu Math20D matlab#4 A91068067 Chris Deotte B06 Exercise 4.1 (a) >> B=[1.2,2.5;4,0.7] B = 1.2000 2.5000 4.0000 0.7000 (b) >> [eigvec,eigval]=eig(B) eigvec = 0.6501 -0.5899 0.7599 0.8075 eigval = 4.1221 0 0 -2.2221 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) (d) 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) (c)
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 >> eig(A) ans = 5.5698 + 0.0000i -4.1999 + 2.6606i -4.1999 - 2.6606i >> [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) It is unstable. The system has three eigenvalues: real number 5.5698 and two complex numbers -4.1999 + 2.6606i , -4.1999 - 2.6606i . Real number is positive, which indicates that solution goes to infinity as t goes to infinity. For two complex solutions, real number component is not equal to zero. Thus solution is not stable. Exercise 4.5 (a) >> A=[-0.0558,-0.9968,0.0802,0.0415; 0.598,-0.115,-0.0318,0;-3.05,0.388,-0.4650,0;0,0.0805,1,0;] A = -0.0558 -0.9968 0.0802 0.0415 0.5980 -0.1150 -0.0318 0 -3.0500 0.3880 -0.4650 0 0 0.0805 1.0000 0 >> [eigvec,eigval]=eig(A) eigvec = 0.1994 - 0.1063i 0.1994 + 0.1063i -0.0172 + 0.0000i 0.0067 + 0.0000i -0.0780 - 0.1333i -0.0780 + 0.1333i -0.0118 + 0.0000i 0.0404 + 0.0000i -0.0165 + 0.6668i -0.0165 - 0.6668i -0.4895 + 0.0000i -0.0105 + 0.0000i 0.6930 + 0.0000i 0.6930 + 0.0000i 0.8717 + 0.0000i 0.9991 + 0.0000i eigval = -0.0329 + 0.9467i 0.0000 + 0.0000i 0.0000 + 0.0000i

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