(Solved): Write the given linear system in matrix form. \( \left(\right. \) Assume \( \mathbf{X}=\left(\begi ...

Write the given linear system in matrix form. \( \left(\right. \) Assume \( \mathbf{X}=\left(\begin{array}{l}x \\ y \\ z\end{array}\right) \).) \[ \begin{array}{l} \frac{d x}{d t}=-3 x+4 y+e^{-t} \sin (2 t) \\ \frac{d y}{d t}=5 x+7 z+4 e^{-t} \cos (2 t) \\ \frac{d z}{d t}=y+6 z-e^{-t} \end{array} \] \[ \mathbf{x}^{\prime}=(\mathrm{x}+(\mathrm{x}+(\mathrm{x}) \]