Let A e Rx4 be a matrix and suppose you know that 2 100 1 100...

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Let A e Rx4 be a matrix and suppose you know that 2 100 1 100 0 0 8 2 0 0 2 8 X = is a solution of the Lyapunov equation AX + XAT = -I. Without solving for A explicitly, can you evaluate etAdt ? If yes, justify each step carefully. If no, why not? Let A e Rx4 be a matrix and suppose you know that 2 100 1 100 0 0 8 2 0 0 2 8 X = is a solution of the Lyapunov equation AX + XAT = -I. Without solving for A explicitly, can you evaluate etAdt ? If yes, justify each step carefully. If no, why not?