GATE EC 2003 Set 1 Q73 — Control Systems

The zero-input response of a system given by the state-space equation

$\left[\begin{array}{l}\dot{x}_{1} \\ \dot{x}_{2}\end{array}\right]=\left[\begin{array}{ll}1 & 0 \\ 1 & 1\end{array}\right]\left[\begin{array}{l}x_{1} \\ x_{2}\end{array}\right]$ and $\left[\begin{array}{l}x_{1}(0) \\ x_{2}(0)\end{array}\right]=\left[\begin{array}{l}1 \\ 0\end{array}\right]$ is