I need help solving this system of equations:
$\dot{x}_1=-3x_1-2x_2\\ \dot{x}_2=2x_2-x_3.$
I'm confused by the inclusion of $x_3$ since we don't have an equation for $\dot{x}_3$. I'm not sure how to make the coefficient matrix for the system without an equation for $\dot{x}_3$.
$x_3$ can be considered as an input function for the system
$$ \left( \begin{array}{c} \dot x_1\\ \dot x_2 \end{array} \right) = \left( \begin{array}{cc} -3& -2\\ 0 & 2 \end{array} \right) \left( \begin{array}{c} x_1\\ x_2 \end{array} \right)+ \left( \begin{array}{c} 0\\ -1 \end{array} \right) x_3 $$