Exercise 29

For each of the matrices $A$ in Finding Eigenvalues and Eigenvectors:

1. Find the characteristic polynomial of $A$.

2. Find all of the eigenvalues of $A$.

3. Find an eigenvector for each eigenvalue of $A$.

$\displaystyle A = \begin{pmatrix} 1 & 2 \\ 0 & 3 \end{pmatrix}$