Answer
See below
Work Step by Step
Given:
$x_1(t)=\begin{bmatrix}
e^t\\
2e^{2t}
\end{bmatrix}$
$x_2(t)=\begin{bmatrix}
4e^t\\
8e^{2t}
\end{bmatrix}$
We can notice that:
$x_2(t)=\begin{vmatrix}
4e^t\\
8e^{2t}
\end{vmatrix}=4\begin{vmatrix}
e^t\\
2e^{2t}
\end{vmatrix}=4x_2(t)$
Hence, $x_1(t),x_2(t)$ and $x_3(t)$ are linearly independent on $(-\infty,\infty)$
