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