Controllable Subsystem: Suppose $(A,b)$ is controllable, and a state space transformation $T$ is applied to yield

$\frac{?}{\text{b}\text{a}\text{r}}(A)=\left[\begin{array}{cc}\frac{?}{\text{b}\text{a}\text{r}}(A{)}_{11}& \frac{?}{\text{b}\text{a}\text{r}}(A{)}_{12}\\ \frac{?}{\text{b}\text{a}\text{r}}(A{)}_{21}& \frac{?}{\text{b}\text{a}\text{r}}(A{)}_{22}\end{array}\right]\frac{,}{b}ar(b)=\left[\begin{array}{c}\frac{?}{\text{b}\text{a}\text{r}}(b{)}_1\\ 0\end{array}\right],$

where $\frac{?}{\text{b}\text{a}\text{r}}(A{)}_{11}\frac{,}{b}ar(b{)}_1$inR.

$($a$)$ points