It's a very easy exercise:

\begin{bmatrix}13 & 16 & 16\\ -5&-7&-6\\-5&-8&-7\end{bmatrix}

compute the Jordan canonical form of the above matrix.

in order to compute the Jordan canonical form, we must use elementary transformation to the below matrix:
\begin{bmatrix} \lambda - 13 & -16 & -16\\ 5& \lambda+7&6\\5&8& \lambda + 7\end{bmatrix}
take the above matrix to diagonal form.
I get the below matrix:
\begin{bmatrix}1 & 0 & 0\\ 0&1&0\\0&0& \lambda^{3}+ \lambda^{2}-21 \lambda -13 \end{bmatrix}
but it looks not right
I want to know the diagonal form of
\begin{bmatrix} \lambda - 13 & -16 & -16\\ 5& \lambda+7&6\\5&8& \lambda + 7\end{bmatrix}
is ?