Q$2.$ Consider linear two systems shown below.

$\frac{dx}{dt}=Ax+Bu,\frac{dz}{dt}=Az+Bu$

Note that the input $u$ is put to both states $x$ and $z$ at the same time. Show that if the matrix A and $B$ are the same in both systems, the total system $(x,z)$ are not controllable. $($Hint: consider an extended state vector $\left[\begin{array}{c}x\\ z\end{array}\right])$