##### 46. Consider the state space model of a system...

46. Consider the state space model of a system, as given below

$\begin{bmatrix}\dot x_1\\\dot x_2\\\dot x_3 \end{bmatrix} = \begin{bmatrix}-1&1&0\\0&-1&0\\0&0&-2\end{bmatrix} \begin{bmatrix} x_1\\ x_2\\ x_3 \end{bmatrix}+ \begin{bmatrix}0\\4\\0 \end{bmatrix}u$ ; $y=\begin{bmatrix}1&1&1\end{bmatrix} \begin{bmatrix}x_1\\x_2\\x_3\end{bmatrix}$

The system is

(A)  controllable and observable

(D)  controllable and unobservable

(C)  uncontrollable and unobservable

(B)  uncontrollable and observable

Hint:

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