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## Homework Statement

[tex]\begin{bmatrix}

-7 && -16 && 4\\

6 && 13 && -2\\

12 && 16 && 1

\end{bmatrix}[/tex]

Diagonalize the matrix (if possible), given that one eigenvalue is 5, and that one eigenvector is {-2, 1, 2}

## Homework Equations

[tex]A=PDP^{-1}[/tex]

## The Attempt at a Solution

If I were allowed to simply calculate the eigenvalues and corresponding eigenvectors, I'd be able to determine if it's diagonalizable and if so, to diagonalize it. The problem here is that I have to go only on the provided information.

I'm stuck regarding how to proceed with this question. Where do I start?

Thanks!