Question

If I can reduce an augmented matrix to \[\left[\begin{matrix}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{matrix}\right]\] were the vectors linearly independent?

Answer 1

The first three vectors were, at least. :)

Answer 2

but to answer your question, no the original 4 vectors are not linearly independent.
However, any 3 of the 4 would be linearly independent.