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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
in Linear Algebra by (1.5k points)
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