Find the Closest Point to Y in the Subspace W

question 3

Multiple Choice

Find the closest point to y in the subspace W spanned by u₁ and u₂.
- $$\mathbf { y } = \left[ \begin{array} { r } 27 \\17 \\7\end{array} \right] , \mathbf { u } _ { 1 } = \left[ \begin{array} { r } 2 \\2 \\- 1\end{array} \right] , \mathbf { u } _ { 2 } = \left[ \begin{array} { r } - 1 \\3 \\4\end{array} \right]$$

• A)
• \(\left[ \begin{array} { c } - 8 \\ 96 \\ 95 \end{array} \right]\)
• B)
• \(\left[ \begin{array} { r } - 16 \\ - 24 \\ 1 \end{array} \right]\)
• C)
• \(\left[ \begin{array} { r } - 5 \\ 31 \\ 34 \end{array} \right]\)
• D)
• \(\left[ \begin{array} { c } 16 \\ 24 \\ - 1 \end{array} \right]\)

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Definitions:

Dream Interpretation

The process of assigning meaning to dreams, often seen in psychoanalysis as a way to uncover underlying thoughts and feelings.

Analytic Introspection

A method in psychology where individuals closely analyze their own thoughts and emotions to gain insight.

Experimentation

A method of testing hypotheses by manipulating and controlling variables to determine cause and effect.

Behaviorism

A field of psychology that focuses on observing and controlling behavior through environmental stimuli and responses, rather than internal thoughts and feelings.