Answer
See below
Work Step by Step
Given:
$x_1(t)=\begin{bmatrix}
t\\
t
\end{bmatrix}$
and $x_2(t)=\begin{bmatrix}
t\\
t^2
\end{bmatrix}$
Obtain:
$W_{[x_1,x_2]}=\begin{vmatrix}
t & t\\
t & t^2
\end{vmatrix}=t^3-t^2$
If we take $W_{[x_1,x_2]}(2)=2^3-2^2=4\ne 0$ for all $t \in (-\infty, \infty)$
Hence, $x_1(t)$ and $x_2(t)$ are linearly independent on $(-\infty,\infty)$
