Determine Whether {V₁, V₂, V₃} Is a Basis for R³

Multiple Choice

Determine whether {v₁, v₂, v₃} is a basis for R³
-Let $\mathrm { A } = \left[ \begin{array} { r r r r r } - 1 & 3 & 7 & 2 & 0 \\ 1 & - 2 & - 7 & - 1 & 3 \\ 2 & - 4 & - 9 & - 5 & 1 \\ 3 & - 6 & - 11 & - 9 & - 1 \end{array} \right]$ and $B = \left[ \begin{array} { r r r r r } 1 & - 3 & - 7 & - 2 & 0 \\ 0 & 1 & 0 & 1 & 3 \\ 0 & 0 & 5 & - 3 & - 5 \\ 0 & 0 & 0 & 0 & 0 \end{array} \right]$
It can be shown that matrix $\mathrm { A }$ is row equivalent to matrix $\mathrm { B }$ . Find a basis for $\mathrm { Col } \mathrm {} \mathrm { A }$ .

A)
$\left[ \begin{array} { l } 1 \\ 0 \\ 0 \\ 0 \end{array} \right] , \left[ \begin{array} { c } - 3 \\ 1 \\ 0 \\ 0 \end{array} \right] , \left[ \begin{array} { c } - 7 \\ 0 \\ 5 \\ 0 \end{array} \right]$

B)
$\left[\begin{array}{r}-1 \\1 \\2 \\3\end{array}\right],\left[\begin{array}{r}3 \\-2 \\-4 \\-6\end{array}\right],\left[\begin{array}{c}7 \\-7 \\-9 \\-11\end{array}\right]$



C)
$\left[ \begin{array} { r } - 1 \\ 1 \\ 2 \\ 3 \end{array} \right] , \left[ \begin{array} { r } 3 \\ - 2 \\ - 4 \\ - 6 \end{array} \right] , \left[ \begin{array} { r } 2 \\ - 1 \\ - 5 \\ - 9 \end{array} \right]$

D)
$\left[\begin{array}{r}-1 \\1 \\2 \\3\end{array}\right],\left[\begin{array}{r}3 \\-2 \\-4 \\-6\end{array}\right],\left[\begin{array}{r}7 \\-7 \\-9 \\-11\end{array}\right],\left[\begin{array}{r}2 \\-1 \\-5 \\-9\end{array}\right],\left[\begin{array}{r}0 \\3 \\1 \\-1\end{array}\right]$