Determine If the Vector P Is in Span S or Aff

question 47

Multiple Choice

Determine if the vector p is in Span S or aff S.
-Let $\mathbf { v } _ { 1 } = \left[ \begin{array} { r } 2 \\ 1 \\ 3 \\ - 2 \end{array} \right] , \mathbf { v } _ { 2 } = \left[ \begin{array} { r } 3 \\ - 1 \\ 0 \\ 4 \end{array} \right] , \mathbf { v } _ { 3 } = \left[ \begin{array} { r } 5 \\ 4 \\ - 1 \\ - 2 \end{array} \right] , \mathbf { p } = \left[ \begin{array} { r } 2 \\ - 3 \\ 7 \\ 2 \end{array} \right]$ , and $\mathrm { S } = \left\{ \mathbf { v } _ { 1 } , \mathbf { v } _ { 2 } , \mathbf { v } _ { 3 } \right\}$ . It can be shown that $S$ is linearly independent.

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

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Definitions:

Behaviorism

A school of psychology that focuses on observable behaviors and the ways in which they're learned or conditioned rather than on internal processes like emotions and thoughts.

Cognitive Processes

Mental activities involved in acquiring, processing, and storing knowledge.

Discrimination

Unfair or prejudiced treatment of individuals or groups based on characteristics such as race, gender, age, or sexual orientation.

Neutral Stimulus

A stimulus that initially does not elicit any intrinsic response until it is associated with an unconditioned stimulus in classical conditioning.