The general solution is \[\mathbf{x}(t)=C_1e^{t}\begin{pmatrix}2\\1\\\end{pmatrix}+C_2e^{t}\left[t\begin{pmatrix}2\\1\end{pmatrix}+\begin{pmatrix}1\\0\end{pmatrix}\right]\] and the fundamental matrix is \[\begin{pmatrix}2e^{t}&(2t+1)e^{t}\\e^{t}&te^{t}\end{pmatrix}\]