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) $\mathbf { y } = 7 \mathbf { v } _ { 1 } + 3 \mathbf { v } _ { 2 } - 4 \mathbf { v } _ { 3 }$

Question

Quizplus · Accepted Answer

To find an affine combination of $\mathbf{v}_1, \mathbf{v}_2, \mathbf{v}_3$ that equals $\mathbf{y}$, we can set up and solve a system of equations or directly verify the given options. Option A correctly represents $\mathbf{y}$ as an affine combination of the vectors, as confirmed by multiplying each vector by its respective scalar and adding the results to get $\mathbf{y}$.

Write Y as an Affine Combination of the Other Points