Write Y as an Affine Combination of the Other Points

question 33

Multiple Choice

Write y as an affine combination of the other points listed.
- $\mathbf { v } _ { 1 } = \left[ \begin{array} { l } 1 \\ 1 \\ 2 \end{array} \right] , \mathbf { v } _ { 2 } = \left[ \begin{array} { r } 0 \\ 4 \\ - 2 \end{array} \right] , \mathbf { v } _ { 3 } = \left[ \begin{array} { r } 1 \\ - 5 \\ 1 \end{array} \right] , \mathbf { y } = \left[ \begin{array} { r } 5 \\ - 23 \\ 16 \end{array} \right]$

• A) \(\mathbf { y } = 3 \mathbf { v } _ { 1 } - 4 \mathbf { v } _ { 2 } + 2 \mathbf { v } _ { 3 }\)
• B) \(\mathbf { y } = - 3 \mathbf { v } _ { 1 } - 2 \mathbf { v } _ { 2 } + 6 \mathbf { v } _ { 3 }\)
• C) \(\mathbf { y } = 2 \mathrm { v } _ { 1 } + 3 \mathrm { v } _ { 2 } - 4 \mathrm { v } _ { 3 }\)
• D) \(\mathbf { y } = 7 \mathbf { v } _ { 1 } + 3 \mathbf { v } _ { 2 } - 4 \mathbf { v } _ { 3 }\)

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