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I need a little help with an eigen vector question,

The question

Let $M =\left|\begin{matrix} 1 & 1 \\ -36 & 13 \end{matrix}\right|$

Find formulas for the entries of $M^n$, where $n$ is a positive integer

The resulting matrix is a $2\times2$ matrix

What I got so Far

I found that there is one eigen value which is $7$ and I believe I found an eigen vector which is $\langle1,-6\rangle$ (Please double check)

However I'm confused as to what to do next

Can some please enlighten me?

Thanks

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That is correct, eigenvector should be $(1,6)$. So $M$ is not diagonalisable only one linearly independent eigenvector). You can find the Jordan Normal form of $M$ instead and use that. –  Any Dec 10 '13 at 3:25

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