I have
$$x' = \begin{pmatrix} 2 && 2 \\ -2 && 2\end{pmatrix}x + \begin{pmatrix}4 \\ 0\end{pmatrix}$$
what steps should I take to solve it?
if this was homogenious system I'd:
1.) find eigenvalues
2.) find eigenvectors
2a.) find generalized eigenvectors (if any)
3.) write the answer properly
but what should be done here? I have never solved these systems before, general represintation does not seem helpful to me, I need real example but was not able to find any.