Chapter 3.2, Problem 12P

$\left(a\right)$ Show that

$x=e^{-t}\left(\begin{array}{l}2t-1\\ t-1\end{array}\right)+\left(\begin{array}{l}6t+2\\ 2t-1\end{array}\right)$

issolution of the system

$x\text{'}=(\begin{array}{l}1-4\\ 1-3\end{array})x+(\begin{array}{l}2t\\ -3\end{array})$,

Satisfying the initial condition

$x\left(0\right)=\left(\begin{array}{l}1\\ -2\end{array}\right)$.

$\left(b\right)$ Use a computer to draw component plots of $x$.