Find a matrix P and a diagonal matrix D such that D = P-1AP.

Question: Let

A= \begin{bmatrix}-1 & 0 & -1 \\ 1 & -2 & 3\\ 0 & 0 & 1 \end{bmatrix}

a) Find a matrix P and a diagonal matrix D such that D = P^-1 AP.

b) Find P^-1 and use it with D and P to write a simple matrix expression for A^99

Solution:

last expression further can be solved by matrix multiplication

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