Chapter 8.1, Problem 18E

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 (−∞, ∞).

18. $X_1=\left(\begin{array}{c}1\\ -1\end{array}\right)e^t,X_2=\left(\begin{array}{c}2\\ 6\end{array}\right)e^t+\left(\begin{array}{c}8\\ -8\end{array}\right)t{e}^t$