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

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)
$$\left\{\left[\begin{array}{l}2 \\1 \\0 \\0\end{array}\right],\left[\begin{array}{c}\frac{29}{3} \\0 \\-\frac{4}{3} \\1\end{array}\right]\right\}$$