Question: A set of vectors in \({{R}^{n}}\) is given. Determine whether the set is a generating set for \({{R}^{n}}\)

\[\left\{ \left[ \begin{matrix} 1 \\ 1 \\ -1 \\ 1 \\ \end{matrix} \right],\left[ \begin{matrix} 1 \\ 0 \\ 0 \\ 2 \\ \end{matrix} \right],\left[ \begin{matrix} 1 \\ 3 \\ -2 \\ 1 \\ \end{matrix} \right] \right\}\]