Find a basis for the column space of the matrix
\[\begin{bmatrix} -4 & 12 & 1 & 2 \\ 3 & -9 & 4 & -5 \\ 2 & -6 & 4 & 3 \end{bmatrix}.\]Click for answer
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\[ \begin{bmatrix} -4 & 12 & 1 & 2 \\ 3 & -9 & 4 & -5 \\ 2 & -6 & 4 & 3 \end{bmatrix} \]Solution:
\begin{solution} \[ \begin{bmatrix} -4 \\ 3 \\ 2 \end{bmatrix} \qquad \begin{bmatrix} 1 \\ 4 \\ 4 \end{bmatrix} \qquad \begin{bmatrix} 2 \\ -5 \\ 3 \end{bmatrix} \qquad \] \end{solution}