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Consider the continuous-time state equation: \frac{d\mathbf{x}}{dt} = \begin{...

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Consider the continuous-time state equation:

\frac{d\mathbf{x}}{dt} = \begin{bmatrix} -1 & 1 & 0\\2 & 0 & 1\\-1 & 0 & 0\end{bmatrix}\mathbf{x}(t) + \begin{bmatrix} 1\\2\\2\end{bmatrix} u(t),\qquad y(t) = \begin{bmatrix} 1 & 0 & 0\end{bmatrix}\mathbf{x}(t)\frac{d\mathbf{x}}{dt} = \begin{bmatrix} -1 & 1 & 0\\2 & 0 & 1\\-1 & 0 & 0\end{bmatrix}\mathbf{x}(t) + \begin{bmatrix} 1\\2\\2\end{bmatrix} u(t),\qquad y(t) = \begin{bmatrix} 1 & 0 & 0\end{bmatrix}\mathbf{x}(t)

True or false, the system is observable.

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