Consider a continuous time, linear, time invariant system such as i(t) Ax(t) + Bu(t) y(t) = Cr(t) + Du(t) = [8] = -2e-t +2e²t Assume that the state transition matrix is given as e-t+2e2t a) Determine the system matrix A and its eigenvalues. If we set u(t) = 0 for all t, is the system asymptotically stable? Explain. b) Let B = 2e-te²t -e-te²t and show that the system is controllable.

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