Consider the system described by

\[
A=\left[\begin{array}{ccc}
2 & 1 & 1 \\
2 & 3 & 4 \\
-1 & -1 & -2
\end{array}ight] \quad B=\left[\begin{array}{l}
1 \\
2 \\
1
\end{array}ight]
\]

Use Ackermann's formula to design a state feedback controller \(K\) so that the characteristic equation of the system becomes

\[
s^{3}+13 s^{2}+52 s+60=0 \text {. }
\]