Seeing other years' exams, I found an exercise that we never did before (yes, in an exam, the perfect moment to test our creativity).
It's the following:
Consider the linear system $$x'=\begin{bmatrix} -2&1&3 \\ -1&-2&1 \\ 0&0&1 \end{bmatrix}x$$
Give a fundamental matrix to this system, and explain the phase portrait.
I know how to find the fundamental matrix with the exponential matrix or with the eigenvalues and eigenvectors directly, but I don't know how to do the phase portrait of a $3\times 3$ system. We've never did that before.
I'd appreciate any help.