(a) Draw a state diagram for the following state equations:

\[\begin{aligned}& \frac{d x_{1}(t)}{d t}=-2 x_{1}(t)+3 x_{2}(t) \\& \frac{d x_{2}(t)}{d t}=-5 x_{1}(t)-5 x_{2}(t)+2 r(t)\end{aligned}\]

(b) Find the characteristic equation of the system.

(c) Find the transfer functions \(X_{1}(s) / R(s)\) and \(X_{2}(s) / R(s)\).