Find a basis for the column space of the matrix
\[\begin{bmatrix} -3 & 2 & -2 & -18 \\ 1 & -4 & 0 & 12 \\ -1 & 4 & 0 & -12 \end{bmatrix}.\]Click for answer
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\[ \begin{bmatrix} -3 & 2 & -2 & -18 \\ 1 & -4 & 0 & 12 \\ -1 & 4 & 0 & -12 \end{bmatrix} \]Solution:
\begin{solution} \[ \begin{bmatrix} -3 \\ 1 \\ -1 \end{bmatrix} \qquad \begin{bmatrix} 2 \\ -4 \\ 4 \end{bmatrix} \qquad \begin{bmatrix} -2 \\ 0 \\ 0 \end{bmatrix} \qquad \] \end{solution}