Question

Need some help with finding eigenvectors. Matrix to come in following post.

Answer 1

\[\left[\begin{matrix}-i & -4 \\ 1 & -i\end{matrix}\right]\]

I'm not sure how to go about this, \[4\xi_2 = -i \xi_1\]?

I'm trying to find the eigenvector so that I can find the general solution to a system of differential equations.

Answer 2

\[\chi = e^{-t}(\cos t + i \sin t )\left(\begin{matrix}i \\ 1\end{matrix}\right)\]

Is this correct?