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(c) Use your results in (a) to solve the IVP 5 points x' = Ax, Xo = 6=(-1) (a) Use MATLAB to draw the phase portrait for the system x' = Ax 10 points 1. Let A = (a) Find the fundamental matrix o(t) = M1 = X(t)X- 0) using power series. 20 points (b) Check your result by substituting into x' = Ax 5 points (e) Use the eigenvalue, eigenvector method to solve the same IVP above. 20 points Hint: 1) Use eigenvectors and eigenvalues to find the fundamental solution set {xi(t), xz(t)} 2) Write down the nonunique fundamental matrix X(t) = x1(t) xz(t)). 3) Compute the unique X(t)X-0). 4) Obtain the IPV solution using X(t) = X(t)x0)x (t)=A (f) Draw the component plots for the IVP above. 10 points (c) Use your results in (a) to solve the IVP 5 points x' = Ax, Xo = 6=(-1) (a) Use MATLAB to draw the phase portrait for the system x' = Ax 10 points 1. Let A = (a) Find the fundamental matrix o(t) = M1 = X(t)X- 0) using power series. 20 points (b) Check your result by substituting into x' = Ax 5 points (e) Use the eigenvalue, eigenvector method to solve the same IVP above. 20 points Hint: 1) Use eigenvectors and eigenvalues to find the fundamental solution set {xi(t), xz(t)} 2) Write down the nonunique fundamental matrix X(t) = x1(t) xz(t)). 3) Compute the unique X(t)X-0). 4) Obtain the IPV solution using X(t) = X(t)x0)x (t)=A (f) Draw the component plots for the IVP above. 10 points

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