Determine If the Set of Points Is Affinely Dependent A) the Set Is Affinely Dependent

question 37

Multiple Choice

Determine if the set of points is affinely dependent. If so, construct an affine dependence relation for the points.
- $\left[ \begin{array} { r } 4 \\ 8 \\ - 1 \end{array} \right] , \left[ \begin{array} { r } - 8 \\ - 16 \\ 4 \end{array} \right] , \left[ \begin{array} { r } 0 \\ 1 \\ 12 \end{array} \right] , \left[ \begin{array} { r } - 16 \\ - 31 \\ 22 \end{array} \right]$

• A) The set is affinely dependent. \(2 \left[ \begin{array} { r } 4 \\ 8 \\ - 1 \end{array} \right] - 3 \left[ \begin{array} { r } - 8 \\ - 16 \\ 4 \end{array} \right] - \left[ \begin{array} { r } 0 \\ 1 \\ 12 \end{array} \right] + \left[ \begin{array} { r } - 16 \\ - 31 \\ 22 \end{array} \right] = \left[ \begin{array} { l } 0 \\ 0 \\ 0 \end{array} \right]\)
• B) The set is affinely dependent. \(5 \left[ \begin{array} { r } 4 \\ 8 \\ - 1 \end{array} \right] - 3 \left[ \begin{array} { r } - 8 \\ - 16 \\ 4 \end{array} \right] - \left[ \begin{array} { r } 0 \\ 1 \\ 12 \end{array} \right] - \left[ \begin{array} { r } - 16 \\ - 31 \\ 22 \end{array} \right] = \left[ \begin{array} { l } 0 \\ 0 \\ 0 \end{array} \right]\)
• C) The set is affinely dependent. \(2 \left[ \begin{array} { r } 4 \\ 8 \\ - 1 \end{array} \right] + 3 \left[ \begin{array} { r } - 8 \\ - 16 \\ 4 \end{array} \right] + \left[ \begin{array} { r } 0 \\ 1 \\ 12 \end{array} \right] - \left[ \begin{array} { r } - 16 \\ - 31 \\ 22 \end{array} \right] = \left[ \begin{array} { l } 0 \\ 0 \\ 0 \end{array} \right]\)
• D) The set is affinely independent.

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Definitions:

Systematic Desensitization

A behavioral therapy method used to gradually reduce anxiety through the association of a relaxed state with gradually increasing anxiety-triggering stimuli.

Classical Conditioning

A type of learning through which an organism learns to associate one stimulus with another.

Operant Conditioning

A method of learning that employs rewards and punishments for behavior, encouraging the likelihood of a behavior being repeated.

Extinction

In psychology, the gradual weakening and disappearance of a conditioned response when the conditioned stimulus is repeatedly presented without the unconditioned stimulus.