Question: Let A E R4X4 be a matrix and suppose you know that 2 10 0 1 0 0 0 0 8 2 0 0

Let A E R4X4 be a matrix and suppose you know that

Let A E R4X4 be a matrix and suppose you know that 2 10 0 1 0 0 0 0 8 2 0 0 2 8 1 X = is a solution of the Lyapunov equation AX + XAT = -I. Without solving for A explicitly, can you evaluate %3D etA dt ? If yes, justify each step carefully. If no, why not?

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