Consider the initial value problem X₁ x(t) = = dx dt 2-4, ₁- = - || (a) Find the eigenvalues and eigenvectors for the coefficient matrix. 8 [2 2 X, (b) Solve the initial value problem. Give your solution in real form. e2(-6 sin (4t) + 8 cos(4t)) 1 x(0) = [8] and X₂ = 2+41, 0₂: = Use the phase plotter pplane9.m in MATLAB to answer the following question. Spiral, spiraling outward in the counterclockwise direction 1. Describe the trajectory. 1

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