Answer
See below
Work Step by Step
1. Find eigenvalues:
(A-$\lambda$I)$\vec{V}$=$\vec{0}$
$\begin{bmatrix}
2-\lambda & 3\\
0 & 2-\lambda
\end{bmatrix}\begin{bmatrix}
v_1\\
v_2
\end{bmatrix}=\begin{bmatrix}
0\\
0
\end{bmatrix}$
$\begin{bmatrix}
2-\lambda & 3\\
0 & 2-\lambda
\end{bmatrix}=0$
$(\lambda -2) ^2=0$
$\lambda_1=\lambda_2=2$
2. Find eigenvectors:
For $\lambda=2$
let $B=A-\lambda_1I$
$B=\begin{bmatrix}
0 & 3\\
0 & 0
\end{bmatrix}$
Let $r$ be a free variable.
$\vec{V}=r(1,0) \\
E_1=\{(1,0)\}
\rightarrow dim(E_1)=1 \ne 2$
Hence, $A$ is defective.
