Find a Basis for the Column Space of the Matrix $$B = \left[ \begin{array} { r r r r } 1 & - 2 & 5 & - 3 \\2 & - 4 & 13 & - 2 \\- 3 & 6 & - 15 & 9\end{array} \right]$$

question 41

Multiple Choice

Find a basis for the column space of the matrix.
- $$B = \left[ \begin{array} { r r r r } 1 & - 2 & 5 & - 3 \\2 & - 4 & 13 & - 2 \\- 3 & 6 & - 15 & 9\end{array} \right]$$

• A)
• \[
• \left\{\left[\begin{array}{r}
• 1 \\
• 2 \\
• -3
• \end{array}\right],\left[\begin{array}{r}
• 5 \\
• 13 \\
• -15
• \end{array}\right]\right\}
• \]
• B) \[
• \left\{\left[\begin{array}{l}
• 1 \\
• 0 \\
• 0
• \end{array}\right],\left[\begin{array}{l}
• 0 \\
• 1 \\
• 0
• \end{array}\right]\right\}
• \]
• C)
• \[
• \left\{\left[\begin{array}{r}
• 1 \\
• 2 \\
• -3
• \end{array}\right],\left[\begin{array}{r}
• -2 \\
• -4 \\
• 6
• \end{array}\right]\right\}
• \]
• D)
• \[
• \left\{\left[\begin{array}{l}
• 2 \\
• 1 \\
• 0 \\
• 0
• \end{array}\right],\left[\begin{array}{c}
• \frac{29}{3} \\
• 0 \\
• -\frac{4}{3} \\
• 1
• \end{array}\right]\right\}
• \]

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Definitions:

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