In this example, the objective is to demonstrate the effect of trying to transform a system to observable canonical form. Consider the system

\[\mathbf{A}=\left[\begin{array}{ll}3 & 4 \\1 & 2\end{array}ight] \quad \mathbf{C}=\left[\begin{array}{l}1 \\2\end{array}ight]\]

which has been identified before as unobservable.