Theorem LIVRN says we can answer this question by putting theses vectors into a matrix as columns and row-reducing. Doing this we obtain,
\begin{equation*}
\begin{bmatrix}
\leading{1} & 0 & 0\\
0 & \leading{1} & 0\\
0 & 0 & \leading{1}\\
0 & 0 & 0
\end{bmatrix}
\end{equation*}
With $n=3$ (3 vectors, 3 columns) and $r=3$ (3 pivot columns) we have $n=r$ and the theorem says the vectors are linearly independent.