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1. (a) Suppose that A and B are constant square matrices. Show that the state transition matrix for the time-varying system described by i(t) = e-At BeAtx(t) is D(t, s) = e-Ate(A+B)(t-s)As (b) If A is an n x n matrix of full rank, show using the definition of the matrix exponential that eto do = left - nJA-]. Using this result, obtain the solution to the linear time-invariant equation i = Ar + Bu , x(0) = TO where u is a constant r-dimensional vector and B is an (n x r)-dimensional matrix