Question: Prove that \(\left\{\left[\begin{array}{rr}1 & 1 \\ 0 \\ -1 \\ -5\end{array}\right]\left[\begin{array}{r}1 \\ -7 \\ -4 \\ -3\end{array}\right],\left[\begin{array}{r}1 \\ -5 \\ -1 \\ 5\end{array}\right]\right\}\) is a basis

for the column space of the matrix in problem # 3 (see matrix below

\(\left[\begin{array}{rrrrr}-1 & 1 & 2 & 2 & 1 \\ 2 & -2 & -1 & -3 & 2 \\ 1 & -1 & 1 & 1 & 2 \\ 1 & -1 & 4 & 8 & 3\end{array}\right]\) )

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