GATE EC 1992 Set 1 Q1.6 — Control Systems

A linear time-invariant system is described by the state variable model
$$\left[\begin{array}{l} x_{1} \\ x_{2} \end{array}\right]=\left[\begin{array}{rc} -1 & 0 \\ 0 & -2 \end{array}\right]\left[\begin{array}{l} x_{1} \\ x_{2} \end{array}\right]+\left[\begin{array}{l} 0 \\ 1 \end{array}\right] u=\left[\begin{array}{ll} 1 & 2 \end{array}\right]\left[\begin{array}{l} x_{1} \\ x_{2} \end{array}\right]$$