Find a basis for the column space of the matrix
\[\begin{bmatrix} -3 & -3 & -1 & 19 \\ -5 & 4 & 4 & -1 \\ 1 & -2 & -2 & 5 \end{bmatrix}.\]Click for answer
Click for Latex code
\[ \begin{bmatrix} -3 & -3 & -1 & 19 \\ -5 & 4 & 4 & -1 \\ 1 & -2 & -2 & 5 \end{bmatrix} \]Solution:
\begin{solution} \[ \begin{bmatrix} -3 \\ -5 \\ 1 \end{bmatrix} \qquad \begin{bmatrix} -3 \\ 4 \\ -2 \end{bmatrix} \qquad \begin{bmatrix} -1 \\ 4 \\ -2 \end{bmatrix} \qquad \] \end{solution}