A system has the differential equations

\(\left[\begin{array}{lll}5 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 2\end{array}\right]\left[\begin{array}{c}\ddot{x}_{1} \\ \ddot{x}_{2} \\ \ddot{x}_{3}\end{array}\right]+\left[\begin{array}{ccc}3 & -1 & 0 \\ -1 & 4 & -3 \\ 0 & -3 & 3\end{array}\right]\left[\begin{array}{c}\dot{x}_{1} \\ \dot{x}_{2} \\ \dot{x}_{3}\end{array}\right]+\left[\begin{array}{ccc}50 & -20 & 0 \\ -20 & 100 & -80 \\ 0 & -80 & 120\end{array}\right]\left[\begin{array}{l}x_{1} \\ x_{2} \\ x_{3}\end{array}\right]=\left[\begin{array}{l}0 \\ 0 \\ 0\end{array}\right]\)

Write the system of differential equations as six first-order differential equations.