The problem I'm doing asks me to solve the normal system x'=Ax, but A is an unknown 2x2 matrix. However, I'm given some initial values and:

$\displaystyle

A \left(\begin{array}{r}-1\\4\end{array}\right) = -4 \left(\begin{array}{r}-1\\4\end{array}\right)

$

OK, I know this says -4 is an eigenvalue with corresponding eigenvector (-1,4)

$\displaystyle

A \left(\begin{array}{r}0\\1\end{array} \right) = -4 \left(\begin{array}{r}0\\1\\\end{array} \right)

+ \left( \begin{array}{r}-1\\4\end{array}\right)

$

But I'm not sure what to make of this.

My current approach is to find $\displaystyle e^{At} $ so I need a second, maybe generalized? eigenvector and corresponding eigenvalue.

edit: Never mind, I figured I can just solve for A