Consider a system with the following State-Variable Matrix model:

\[\begin{array}{ll}A=\left[\begin{array}{ccc}0 & 1 & 0 \\0 & 0 & 1 \\-6 & -11 & -6\end{array}ight] \quad B=\left[\begin{array}{l}0 \\0 \\1\end{array}ight] \\C=\left[\begin{array}{lll}6 & 2 & 0\end{array}ight] & D=[0]\end{array}\]

(a) Explain the concepts of controllability and observability

(b) Evaluate the controllability and observability of the system

(c) Show that the system's transfer function is given by

\[T(s)=\frac{2}{s^{2}+3 s+2}\]