Determine If the Vector P Is in Span S or Aff

Multiple Choice

Determine if the vector p is in Span S or aff S.
-Let $\mathbf { v } _ { 1 } = \left[ \begin{array} { r } 2 \\ 1 \\ 3 \\ - 2 \end{array} \right] , \mathbf { v } _ { 2 } = \left[ \begin{array} { r } 3 \\ - 1 \\ 0 \\ 4 \end{array} \right] , \mathbf { v } _ { 3 } = \left[ \begin{array} { r } 5 \\ 4 \\ - 1 \\ - 2 \end{array} \right] , \mathbf { p } = \left[ \begin{array} { r } 10 \\ 12 \\ - 6 \\ - 8 \end{array} \right]$ , and $\mathrm { S } = \left\{ \mathbf { v } _ { 1 } , \mathbf { v } _ { 2 } , \mathbf { v } _ { 3 } \right\}$ . It can be shown that $\mathrm { S }$ is linearly independent.

A) $\mathbf { p } \notin$ span $S$ and $\mathbf { p } \notin$ aff $S$
B) $\mathbf { p } \in$ span $S$ and $\mathbf { p } \notin$ aff $\mathrm { S }$
C) $\mathbf { p } \notin \operatorname { span } S$ and $\mathbf { p } \in$ aff $S$
D) $p \in \operatorname { span } S$ and $p \in$ aff $S$