Find the Closest Point to Y in the Subspace W

question 37

Multiple Choice

Find the closest point to y in the subspace W spanned by u₁ and u₂.
- $$\mathbf { y } = \left[ \begin{array} { r } 16 \\0 \\2\end{array} \right] , \mathbf { u } _ { 1 } = \left[ \begin{array} { r } 1 \\0 \\- 1\end{array} \right] , \mathbf { u } _ { 2 } = \left[ \begin{array} { l } 2 \\1 \\2\end{array} \right]$$

• A)
• \(\left[ \begin{array} { r } 18 \\ 7 \\ 10 \end{array} \right]\)
• B)
• \(\left[ \begin{array} { r } - 15 \\ - 4 \\ - 1 \end{array} \right]\)
• C)
• \(\left[ \begin{array} { r } 15 \\ 4 \\ 1 \end{array} \right]\)
• D)
• \(\left[ \begin{array} { r } 20 \\ 9 \\ 16 \end{array} \right]\)

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