Answer
See below
Work Step by Step
1. Find eigenvalues:
(A-$\lambda$I)$\vec{V}$=$\vec{0}$
$\begin{bmatrix} 13-\lambda & 9\\ 25 & -17-\lambda \end{bmatrix}\begin{bmatrix} v_1\\ v_2 \end{bmatrix}=\begin{bmatrix} 0\\ 0 \end{bmatrix}$
$\begin{bmatrix} 13-\lambda & 9\\ 25 & -17-\lambda \end{bmatrix}=0$
$(13- \lambda)(-17-\lambda)-225=0$
$\lambda_1= \lambda_2=2$
Because A is a $2 \times 2$ matrix and A also has repeated eigenvalues, $A$ is not diagonalizable.
