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.
- $\text { Let } \mathbf{v}_{1}=\left[\begin{array}{r}2 \\1 \\3 \\-2\end{array}\right], \mathbf{v}_{2}=\left[\begin{array}{r}3 \\-1 \\0 \\4\end{array}\right], \mathbf{v}_{3}=\left[\begin{array}{r}5 \\4 \\-1 \\-2\end{array}\right], p=\left[\begin{array}{r}5 \\-3 \\5 \\3\end{array}\right] \text {, and } \mathrm{S}=\left\{\mathbf{v}_{1}, \mathbf{v}_{2}, \mathbf{v}_{3}\right\} \text {. It can be shown that } \mathrm{S} \text { is linearly }$ independent.

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