If the matrix A can be diagonalized, then P1 AP D or A PDP1 . Use this last result and
Chapter 10, Problem 23(choose chapter or problem)
If the matrix A can be diagonalized, then \(\mathbf{P}^{-1} \mathbf{A} \mathbf{P}=\mathbf{D}\) or \(\mathbf{A}=\mathbf{P D P}^{-1}\). Use this last result and (3) to show that \(e^{\mathbf{A} t}=\mathbf{P} e^{\mathbf{D} t} \mathbf{P}^{-1}\).
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