The general solution is \[\mathbf{x}(t)=C_1e^{-t}\begin{pmatrix}1\\2\\\end{pmatrix}+C_2e^{2t}\begin{pmatrix}2\\1\end{pmatrix}\] and the fundamental matrix is \[\begin{pmatrix}e^{-t}&2e^{2t}\\2e^{-t}&e^{2t}\end{pmatrix}\]The critical point \((0,0)\) is a saddle point and unstable. Refer to the video for a sketch of the phase portrait.