Find a basis for the column space of the matrix
\[\begin{bmatrix} 2 & 2 & -3 & -15 \\ -1 & 3 & -5 & -7 \\ 1 & 2 & -2 & -10 \end{bmatrix}.\]Click for answer
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\[
\begin{bmatrix}
2 & 2 & -3 & -15 \\
-1 & 3 & -5 & -7 \\
1 & 2 & -2 & -10
\end{bmatrix}
\]
Solution:
\begin{solution}
\[
\begin{bmatrix}
2 \\
-1 \\
1
\end{bmatrix} \qquad
\begin{bmatrix}
2 \\
3 \\
2
\end{bmatrix} \qquad
\begin{bmatrix}
-3 \\
-5 \\
-2
\end{bmatrix} \qquad
\]
\end{solution}