Find the state vector via the formal-solution approach. (dot{mathbf{x}}=left[begin{array}{cc}5 & 1 -4 & 1end{array} ight] mathbf{x}+left[begin{array}{c}1

Find the state vector via the formal-solution approach.

\(\dot{\mathbf{x}}=\left[\begin{array}{cc}5 & 1 \\ -4 & 1\end{array}\right] \mathbf{x}+\left[\begin{array}{c}1 \\ -1\end{array}\right] u, \quad u=\sin t, \quad \mathbf{x}(0)=\left\{\begin{array}{l}0 \\ 1\end{array}\right\}\)