Calculate eigenvectors I am given the $2\times2$ matrix  $$A = \begin {bmatrix} -2&-1 \\\\ 15&6 \ \end{bmatrix}$$
I calculated the Eigenvalues to be 3 and 1. How do I find the vectors? If I plug the value back into the character matrix, I get $$B = \begin {bmatrix} -5&1 \\\\ 15&3 \ \end{bmatrix}$$
Am I doing this right? What would the eigenvector be?

Remember what the word "eigenvector" means.  If $3$ is an eigenvalue, then you're looking for a vector satisfying this:
$$A = \begin {bmatrix} -2&-1 \\\\ 15&6 \ \end{bmatrix}\begin{bmatrix} x \\ y\end{bmatrix} = 3\begin{bmatrix} x \\ y\end{bmatrix}$$
Solve that.  You'll get infinitely many solutions since every scalar multiple of a solution is also a solution.
