The state variable description of a single input single output linear system is given by

where

\[
\begin{aligned}
\dot{x}(t) & =\mathrm{A} x(t)+\mathrm{B} u(t) \\
y(t) & =\mathrm{C} x(t) \\
\mathrm{A} & =\left[\begin{array}{ll}
1 & 1 \\
2 & 0
\end{array}ight], \quad \mathrm{B}=\left[\begin{array}{l}
0 \\
1
\end{array}ight] \text { and } \mathrm{C}=\left[\begin{array}{ll}
1 & -1
\end{array}ight]
\end{aligned}
\]

The system is
(a) controllable and observable
(b) controllable but unobservable
(c) uncontrollable but observable
(d) uncontrollable and unobservable