Chapter 3.5, Problem 8P

In each of Problems 7through $12$, find the solution of the given initial value problem. Draw the trajectory of the solution in the $x_1{x}_2-$ plane and also draw the component plots of $x_1$ versus $t$ and of $x_2$ versus $t$.

$X\text{'}=\left(\begin{array}{cc}-\frac{5}{2}& \frac{3}{2}\\ -\frac{3}{2}& \frac{1}{2}\end{array}\right)X,X\left(0\right)=\left(\begin{array}{l}3\\ -1\end{array}\right)$.