Question

Show that the following elements spans R^3:

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

Answer 1

You need to find three independent vectors. You could form a matrix and row reduce and look for Rank 3 (i.e. three pivots).

Answer 2

Just for the sake of an alternative :

Show that the scalar triple product of any 3 of the given vectors is nonzero.