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

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)
$$\left\{ \left[ \begin{array} { l } 1 \\0 \\0 \\0\end{array} \right] , \left[ \begin{array} { l } 0 \\1 \\0 \\0\end{array} \right] \right\}$$