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:

Right Ventricle

The chamber of the heart responsible for pumping deoxygenated blood to the lungs for gas exchange.

Cardiac Muscle Cells

Specialized muscle cells found in the heart that contract rhythmically to pump blood throughout the body.

Skeletal Muscle Cells

Long, cylindrical cells that make up skeletal muscles, capable of contraction and responsible for voluntary movements.

Action Potential Propagation

The process by which an electrical impulse travels along the membrane of a neuron or muscle fiber, enabling the transmission of signals over long distances within the body.