Chapter 6.3, Problem 28E

To determine

The solution of the system $\{\begin{array}{l}{x}^{\prime }=2x+4y-2z\\ y^{\prime }=x-y\\ z^{\prime }=2x-2y\end{array}$ for the given fundamental matrix $\Phi \left(t\right)=\left(\begin{array}{ccc}-e^{-2t}& 0& 1\\ e^{-2t}& e^{-t}& 1\\ 2e^{-2t}& 2e^{-2t}& 1\end{array}\right)$ with the initial condition $x\left(0\right)=-1,y\left(0\right)=\text{0 and }z\left(0\right)=1$ and graph it.