Select all statements that apply. Wrong choices will be penalized.
For a system given by:
$\begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & -1 & 0 & 0 \\ 1 & 0 & 3 & 0 \\ -2 & 0 & 0 & -1 \end{bmatrix}$, $B = \begin{bmatrix} -1 \\ 1 \\ 1 \\ 2 \end{bmatrix}$, $C = \begin{bmatrix} 1 & 0 & 1 & 0 \end{bmatrix}$
Controllable and stable
Controllable and unstable
Uncontrollable and unstable
Uncontrollable and stabilizable
Uncontrollable and unstabilizable
Eigenvalues can be placed as \{$-1, -2, -2 \pm j$\}
Eigenvalues can be placed as \{$-1 \pm j, -2 \pm j$\}
Eigenvalues can be placed as \{$-1, -1 \pm j, -2$\}