Chapter 3.4, Problem 12P

Phase Portraits and component Plots. In each of Problems $11$ and $12$:

(a) Find the eigenvalues of the given system.

(b) Choose an initial point (other than the origin) and sketch the corresponding trajectory in the $x_1{x}_2$- plane.

(c) For your trajectory in part (b), sketch the graphs of $x_1$ versus $t$ and of $x_2$ versus $t$.

$\text{x}\text{'}=\left(\begin{array}{cc}-\frac{4}{5}& 2\\ -1& \frac{6}{5}\end{array}\right)\text{x}$