Matlab assignment 4

Matlab assignment 4 - Anna Dang PID: A09192411 Math 20D...

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Anna Dang PID: A09192411 Math 20D Professor: Bin Dong TA’s name: Zezhon Zhang (section: A01) Matlab Assignment 4 Exercise4.1 a. Input: >> B = [1.2, 2.5; 4, 0.7] Output: B = 1.2000 2.5000 4.0000 0.7000 b. Input: >> eig(B) >> [eigvec,eigval] = eig(B) Output: ans = 4.1221 -2.2221 eigvec = 0.6501 -0.5899 0.7599 0.8075

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eigval = 4.1221 0 0 -2.2221 Exercise4.2 a. The matrix A : b. Input: >> A =[1,3;-1,-8] >> eig(A) >> [eigvec,eigval] = eig(A) Output: A = 1 3 -1 -8 ans = 0.6533 -7.6533 eigvec = 0.9934 -0.3276 -0.1148 0.9448
eigval = 0.6533 0 0 -7.6533 c. General solution: The behavior of the solution depends upon the initial conditions. If C 2 =0, the solution becomes unbound as t → ∞ And if C2 ≠ 0, C1 =0, then the solution approach to 0 when t → ∞ d. Graph:

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y ' = - x - 8 y -2 -1 0 1 2 3 4 -4 -3 -2 -1 0 1 2 x y As t increases, the solutions go to infinity because of the exponential function in the general solution of the system. The initial points cause C1 to be zero are precisely to those that lie on the plane determined by two eigenvectors, so the solution starts on this plane approach to the origin when t → ∞. Exercise4.3
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Matlab assignment 4 - Anna Dang PID: A09192411 Math 20D...

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