+1 vote

The state variable formulation of a system is given as

$\begin{bmatrix} x^\cdot_1 \\ x^\cdot_2 \end{bmatrix}=\begin{bmatrix} -2 & 0\\ 0 & -1 \end{bmatrix}\begin{bmatrix} x_1\\ x_2 \end{bmatrix}+\begin{bmatrix} 1\\ 1 \end{bmatrix}u$  ,  $x_1(0)=0$  ,  $x_2(0)=0$ and $y=\begin{bmatrix} 1 & 0 \end{bmatrix}\begin{bmatrix} x_1\\ x_2 \end{bmatrix}$

The system is

1. controllable but not observable
2. not controllable but observable
3. both controllable and observable
4. both not controllable and not observable

edited