Find a Basis for the Column Space of the Matrix $$B = \left[ \begin{array} { r r r r r } 1 & 0 & - 5 & 0 & - 3 \\0 & 1 & 4 & 0 & 4 \\0 & 0 & 0 & 1 & 1 \\0 & 0 & 0 & 0 & 0\end{array} \right]$$

question 81

Multiple Choice

Find a basis for the column space of the matrix.
- $$B = \left[ \begin{array} { r r r r r } 1 & 0 & - 5 & 0 & - 3 \\0 & 1 & 4 & 0 & 4 \\0 & 0 & 0 & 1 & 1 \\0 & 0 & 0 & 0 & 0\end{array} \right]$$

• A) \(\left\{ \left[ \begin{array} { l } 1 \\ 0 \\ 0 \\ 0 \end{array} \right] , \left[ \begin{array} { l } 0 \\ 1 \\ 0 \\ 0 \end{array} \right] , \left[ \begin{array} { r } - 5 \\ 4 \\ 0 \\ 0 \end{array} \right] \right\}\)
• B)
• \[\left\{ \left[ \begin{array} { l }
• 1 \\
• 0 \\
• 0 \\
• 0
• \end{array} \right] , \left[ \begin{array} { l }
• 0 \\
• 1 \\
• 0 \\
• 0
• \end{array} \right] , \left[ \begin{array} { l }
• 0 \\
• 0 \\
• 1 \\
• 0
• \end{array} \right] \right\}\]
• C)
• \[\left\{ \left[ \begin{array} { r }
• 5 \\
• - 4 \\
• 1 \\
• 0 \\
• 0
• \end{array} \right] , \left[ \begin{array} { r }
• 3 \\
• - 4 \\
• 0 \\
• - 1 \\
• 1
• \end{array} \right] \right\}\]
• D)
• \[\left\{ \left[ \begin{array} { l }
• 1 \\
• 0 \\
• 0 \\
• 0
• \end{array} \right] , \left[ \begin{array} { l }
• 0 \\
• 1 \\
• 0 \\
• 0
• \end{array} \right] \right\}\]

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