Chapter 9.6, Problem 13E

In Problems 13 and 14, find the solution to the given system that satisfies the given initial condition.

$x^{\prime }\left(t\right)=\left[\begin{array}{cc}-3& -1\\ 2& -1\end{array}\right]x\left(t\right)$,

a. $x\left(0\right)=\left[\begin{array}{c}-1\\ 0\end{array}\right]$

b. $x\left(\pi \right)=\left[\begin{array}{c}1\\ -1\end{array}\right]$

c. $x\left(-2\pi \right)=\left[\begin{array}{c}2\\ 1\end{array}\right]$

d. $x\left(\frac{\pi }{2}\right)=\left[\begin{array}{c}0\\ 1\end{array}\right]$