Estimated state feedback controller design

We consider the system

$\frac{d}{dt}x=Ax+Bu$

$y=Cx$

with

$A=\left[\begin{array}{ccc}-0\mathrm{.}1078& 0\mathrm{.}2060& -0\mathrm{.}4538\\ 0\mathrm{.}1555& -0\mathrm{.}4682& -0\mathrm{.}4029\\ -0\mathrm{.}3288& -0\mathrm{.}2231& 0\mathrm{.}3235\end{array}\right],B=\left[\begin{array}{c}0\mathrm{.}1948\\ -0\mathrm{.}1829\\ 0\mathrm{.}4502\end{array}\right],$

and

$C=\left[\begin{array}{ccc}-0\mathrm{.}4656& -0\mathrm{.}0613& -0\mathrm{.}1184\end{array}\right].$

We are interested in designing an estimated state feedback controller for this system, using $u$ as the control input and $y$ as the system's output.

$($a$)$ Design a linear observer by placing its closed$-$loop eigenvalues at $(-1,-1,-1).$

$($b$)$ Design a full state$-$feedback controller by placing the closed$-$loop eigenvalues at $(-2,-2,-2).$

$($c$)$ Based on your work so far, compute the transfer function of the single$-$input, single$-$output controller obtained by combining the foregoing observer and full state$-$feedback controller. What are the eigenvalues of the closed$-$loop system?

$($d$)$ Repeat the previous three questions by placing the eigenvalues of the observer at $(-2,-2,-2)$ and the closed$-$loop eigenvalues of the full state$-$feedback controller at $(-1,-1,-1).$

$($e$)$ Are the two controllers the same?