# Math Help - Question regarding a system of DE's and eigenvalues.

1. ## Question regarding a system of DE's and eigenvalues.

Dear Colleagues,

Show that if $w$ is not an eigenvalue of an $n\times n$ constant matrix $A$, then $x(t)$ $=$ $k$ $e^{wt}$ is a solution of
$x^{\prime}(t)$ $=$ $A$ $x(t)$ - $b$ $e^{wt}$,
where $b$ and $k$ are $n\times 1$ constant vectors.

Best Regards,

Raed.

2. Substitute x =k e^{ wt } in the equation. You'll obtain wk = Ak - b .

If w is not an eigenvalue of A then, you can choose k = (A-w I )^{ -1 } b .