Determine Whether {V1, V2, V3} Is a Basis For , And

Multiple Choice

Determine whether {v1, v2, v3} is a basis for
$\mathbf { b } _ { 1 } = \left[ \begin{array} { l } 1 \\ 1 \end{array} \right] , \mathbf { b } _ { 2 } = \left[ \begin{array} { r } 1 \\ - 1 \end{array} \right] , \mathbf { x } = \left[ \begin{array} { r } 3 \\ - 5 \end{array} \right]$ , and $B = \left\{ \mathbf { b } _ { 1 } , \mathbf { b } _ { 2 } \right\}$



- $$B = \left\{ \left[ \begin{array} { r } 1 \\- 3 \\- 3\end{array} \right] , \left[ \begin{array} { r } - 3 \\8 \\- 3\end{array} \right] , \left[ \begin{array} { r } 2 \\- 2 \\2\end{array} \right] \right\} , [ \mathrm { x } ] B = \left[ \begin{array} { r } - 4 \\2 \\- 3\end{array} \right]$$

A)
$\left[ \begin{array} { r } - 10 \\ 34 \\ 8 \end{array} \right]$

B)
$\left[ \begin{array} { r } 0 \\ 6 \\ 12 \end{array} \right]$

C)
$\left[ \begin{array} { r } 8 \\ - 32 \\ 0 \end{array} \right]$

D)
$\left[ \begin{array} { r } - 16 \\ 34 \\ 0 \end{array} \right]$