A linear system

\[\begin{aligned}\dot{\mathbf{x}} & =\mathbf{A x}+\mathbf{B u} \\\mathbf{y} &=\mathbf{C x}+\mathbf{D u}\end{aligned}\]

has \(\mathbf{D}=\mathbf{0}\), where the plant and input matrices \((\mathbf{A}, \mathbf{B})\) are given by \[
(\mathbf{A}, \mathbf{B})=\left(\left[\begin{array}{ccc}
3 & -2 & 0 \\
0 & 0 & 1 \\
4 & -3 & 0 \end{array}ight],\left[\begin{array}{l}
1 \\
0 \\
1 \end{array}ight]ight)
\]

(a) Discuss the controllability and stability of this system.

(b) Determine the feedback matrix \(K\) that will place the poles of the system at \(-1,-1 \pm j\).