1. Suppose $A$ is the $2\times 2$ matrix \begin{equation*} A=\begin{bmatrix} -5 & 8\\-4 & 7 \end{bmatrix} \end{equation*} Find the eigenvalues of $A$.
2. For each eigenvalue of $A$, find the corresponding eigenspace.
3. For the polynomial $p(x)=3x^2-x+2$ and $A$ from above, compute $p(A)$.