Determine If the Vector P Is in Span S or Aff

question 20

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 \(S\)

---

Definitions:

World Price

The international market price of a good or service, influenced by global supply and demand conditions.

Domestic Quantity

The total amount of a goods or services produced and consumed within a country's borders.

Trade

The exchange of goods, services, or both between parties, usually on the basis of comparative advantage.

Absence of Trade

A situation or condition in which there is no exchange of goods or services between people or entities.