Answer
The eigenspace is 1 dimensional subspace of $R^2$
Basis is $\Big\{\begin{bmatrix}
-1\\
3
\end{bmatrix}
\Big\}$
Work Step by Step
$A-10I=\begin{bmatrix}
-6&-2\\
-3&-1
\end{bmatrix}$
Row reduce augmented matrix for $(A-10I)x=0$
$\begin{bmatrix}
1&\frac{1}{3}&0\\
0&0&0
\end{bmatrix}$
$x_1=-\frac{1}{3}x_2$
$x_2$ is free
The eigenspace is 1 dimensional subspace of $R^2$
Basis is $\Big\{\begin{bmatrix}
-1\\
3
\end{bmatrix}
\Big\}$
