I’m trying to diagonalize the following matrix:
$$ A = \left[
\begin{matrix}
1&3\\
4&2
\end{matrix}
\right] $$
I’ve found the eigenvalues to be:
$$ \lambda = 2$$
$$ \lambda = 1$$
For $\text{$\lambda=2$}$, the eigenvector I have is
$$\left[
\begin{matrix}
3\\
1
\end{matrix}
\right]$$
But for $\text{$\lambda=1$}$, I am getting an eigenvector of:
$$\left[
\begin{matrix}
0\\
0
\end{matrix}
\right]$$
Are my eigenvalues wrong or does this just mean that I can’t diagonalize the matrix $A$?