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

question 34

Multiple Choice

Determine if the set of points is affinely dependent. If so, construct an affine dependence relation for the points.
- $$\left[ \begin{array} { l } 4 \\8\end{array} \right] , \left[ \begin{array} { l } 8 \\4\end{array} \right] , \left[ \begin{array} { l } 5 \\7\end{array} \right]$$

• A) The set is affinely dependent. \(3 \left[ \begin{array} { l } 4 \\ 8 \end{array} \right] - \left[ \begin{array} { l } 8 \\ 4 \end{array} \right] + 4 \left[ \begin{array} { l } 5 \\ 7 \end{array} \right] = \left[ \begin{array} { l } 0 \\ 0 \end{array} \right]\)
• B) The set is affinely independent.
• C) The set is affinely dependent. \(3 \left[ \begin{array} { l } 1 \\ 2 \end{array} \right] + \left[ \begin{array} { l } 2 \\ 1 \end{array} \right] - \left[ \begin{array} { l } 5 \\ 7 \end{array} \right] = \left[ \begin{array} { l } 0 \\ 0 \end{array} \right]\)
• D) The set is affinely dependent. \(3 \left[ \begin{array} { l } 4 \\ 8 \end{array} \right] + \left[ \begin{array} { l } 8 \\ 4 \end{array} \right] - 4 \left[ \begin{array} { l } 5 \\ 7 \end{array} \right] = \left[ \begin{array} { l } 0 \\ 0 \end{array} \right]\)

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Definitions:

Language Development

The process by which children come to understand and communicate language during early childhood.

Functional Fixedness

A bias in cognition that confines a person to employ an object exclusively in its customary use, obstructing the process of generating creative solutions.

Mental Sets

Mental sets refer to the tendency to approach situations in a certain way because that method worked in the past, potentially preventing us from seeing alternative solutions.

Effective Problem Solving

A process of defining a problem, generating solutions, and choosing the best course of action to address the issue at hand.