Matlab 6 - MATLAB Assignment 6 Systems of ODEs Exercise...

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MATLAB Assignment 6 Systems of ODEs Exercise 6.1 (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 6.2 (a) (b) >> A=[1,3;-1,-5] A = 1 3 -1 -5 >> [eigvec,eigval]=eig(A) eigvec =
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0.9836 -0.4823 -0.1805 0.8760 eigval = 0.4495 0 0 -4.4495 (c) Exercise 6.3 x ' = 2 y ' = - 3 -2 -1 0 1 2 3 4 -4 -3 -2 -1 0 1 2 x y When x' is negative, the arrows point up and if it is positive, they point downwards. When y' is negative, the arrows point to the right and when it is positive, they point
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towards the left. As the magnitude of y' increases, the slope of the arrows increases and the greater x' is, the larger the horizontal slope. Exercise 6.4 x ' = y y ' = - x -10 -8 -6 -4 -2 0 2 4 6 8 10 -10 -8 -6 -4 -2 0 2 4 6 8 10 x y Exercise 6.5
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x ' = x + 3 y y ' = - x - 5 y -10 -8 -6 -4 -2 0 2 4 6 8 10 -10 -8 -6 -4 -2 0 2 4 6 8 10 x y As t increases, the solutions go to infinity because of the exponential function in the general solution of the system. Exercise 6.6 >> A=[-1,3;0,-2] A = -1 3 0 -2 >> [eigvec,eigval]=eig(A)
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eigvec = 1.0000 -0.9487 0 0.3162
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