1. ## Bases

You forgot the leading [ MATH ] for you Latex- but then you didn't use LaTex code, anyway. Click on $\begin{bmatrix}0 & 0 & -2 \\ 1 & 2 & 1 \\ 1 & 0 & 3\end{bmatrix}$ to see the code.
can you solve the equation $\left|\begin{array}{ccc}-\lambda & 0 & -2 \\1 & 2- \lambda & 1 \\1 & 0 & 3- \lambda\end{array}\right|= 0$? That reduces to solving a cubic equation. I recommend expanding the determinant on the first row.