Diagonalization & Matrix Powers · Medium problem

Solve $\mathbf{x}' = A\mathbf{x}$ with $A = \begin{pmatrix}0 & 1\\4 & 0\end{pmatrix}$ and $\mathbf{x}(0) = \begin{pmatrix}1\\0\end{pmatrix}$. Find the first component $x_1(t)$ at $t = \ln 3$.