## Determine a Matrix From Its Eigenvalue

## Problem 259

Let

\[A=\begin{bmatrix}

a & -1\\

1& 4

\end{bmatrix}\]
be a $2\times 2$ matrix, where $a$ is some real number.

Suppose that the matrix $A$ has an eigenvalue $3$.

**(a)** Determine the value of $a$.

**(b)** Does the matrix $A$ have eigenvalues other than $3$?