Chapter 9.2, Problem 3P

Problems

For Problems 1-5, show that the given vector functions are linearly independent on 
 $\left(-\infty ,\infty \right)$.

 $x_1\left(t\right)=\left[\begin{array}{c}t+1\\ t-1\\ 2t\end{array}\right]$, 
 $x_2\left(t\right)=\left[\begin{array}{c}{e}^t\\ e^{2t}\\ e^{3t}\end{array}\right]$, 
 $x_3\left(t\right)=\left[\begin{array}{c}1\\ \sin t\\ \cos t\end{array}\right]$.