Linear systems

Solve $\dot{\mathbf{x}} = \begin{pmatrix}0 & 1\\-1 & 0\end{pmatrix}\mathbf{x} + \begin{pmatrix}0\\1\end{pmatrix}$, $\mathbf{x}(0) = \mathbf{0}$. (a) Compute $e^{tA}$. (b) Use Duhamel's formula. (c) Check against the equilibrium.