A regulation system has a plant with the transfer function

$$G\left(s\right)=\frac{Y\left(s\right)}{U\left(s\right)}=\frac{5}{s^3+3s^2+4s+6}$$

a. Transform the plant transfer function into the state-space form with the state vector $x={\left[\begin{array}{ccc}y& \dot{y}& \ddot{y}\end{array}\right]}^T$.

b. Determine the state-feedback gain matrix $K$ such that the closed-loop poles are located at $p_{1,2}=-3\pm 4j$ and $p_3=-8$.

c. Verify the result in Part (b) by using the MATLAB command place.