Consider the following continuous$-$time LTI system

$x^{}(t)=Ax(t)+Bu(t)$

where

$A=\left[\begin{array}{ccc}1& -1& 0\\ -1& 2& -1\\ 0& -1& 1\end{array}\right]$

and

$B=\left[\begin{array}{cc}1& 0\\ 0& 1\\ 1& 0\end{array}\right]$

Note, the A matrix in this problem is the same as the A matrix in Problem $4$ of HW$-6.$ Now, do the following:

a$)$ Determine if the system is controllable. Which modes are controllable?

b$)$ Which of the following states can be reached from origin in finite time by designing appropriate input?

$\left[\begin{array}{c}7\\ 7\\ 7\end{array}\right],or,\left[\begin{array}{c}7\\ 0\\ -7\end{array}\right]$