Chapter 9.4, Problem 21E

In Problems 21-24, the given vector functions are solutions to a system $x^{\prime }\left(t\right)=Ax\left(t\right)$. Determine whether they form a fundamental solution set. If they do, find a fundamental matrix for the system and give a general solution.

$x_1=e^{2t}\left[\begin{array}{c}1\\ -2\end{array}\right]\text{, }{x}_2=e^{2t}\left[\begin{array}{c}-2\\ 4\end{array}\right]$