How can I find all values of k which make this matrix diagonalizable over the complex field?

Question

\begin{bmatrix} {0} & {1} & {0}\\ {0} & {0} & {1}\\ {0} & {-k-9} & {k+10} \end{bmatrix}

I have no idea how to go about this problem. I can find eigenvalues in terms of k, but I don't know how to find which k make it diagonalizable.

Answer 1

HINT

If it has distinct eigenvalues, it is diagonalizable, and if it doesn't, it might not be... but this amounts to only one case you need to check.