## Given Eigenvectors and Eigenvalues, Compute a Matrix Product (Stanford University Exam)

## Problem 181

Suppose that $\begin{bmatrix}

1 \\

1

\end{bmatrix}$ is an eigenvector of a matrix $A$ corresponding to the eigenvalue $3$ and that $\begin{bmatrix}

2 \\

1

\end{bmatrix}$ is an eigenvector of $A$ corresponding to the eigenvalue $-2$.

Compute $A^2\begin{bmatrix}

4 \\

3

\end{bmatrix}$.

(*Stanford University Linear Algebra Exam Problem*)

Read solution