Chapter 8.1, Problem 20E

In Problems 17–20 the given vectors are solutions of a system X′ = AX. Determine whether the vectors form a fundamental set on the interval (−∞, ∞).

20. $\begin{array}{ccc}{X}_1=\left(\begin{array}{r}\hfill 1\\ \hfill 6\\ \hfill -13\end{array}\right),& X_2=\left(\begin{array}{c}1\\ -2\\ -1\end{array}\right)e^{-4t},& X_3=\left(\begin{array}{r}\hfill 2\\ \hfill 3\\ \hfill -2\end{array}\right)\end{array}{e}^{3t}$