Express the vector x as a linear combination of the uʹs.
-$$\mathbf { u } _ { 1 } = \left[ \begin{array} { r }
2 \
- 4
\end{array} \right] , \mathbf { u } _ { 2 } = \left[ \begin{array} { r }
12 \
6
\end{array} \right] , \mathbf { x } = \left[ \begin{array} { c }
32 \
- 4
\end{array} \right]$$
A) $\mathbf { x } = 4 \mathbf { u } _ { 1 } + 2 \mathbf { u } _ { 2 }$
B) $\mathbf { x } = - 4 \mathbf { u } _ { 1 } - 2 \mathbf { u } _ { 2 }$
C) $\mathbf { x } = 2 \mathbf { u } _ { 1 } + 4 \mathbf { u } _ { 2 }$
D) $\mathbf { x } = 4 \mathbf { u } _ { 1 } - 2 \mathbf { u } _ { 2 }$

Question

Express the vector x as a linear combination of the uʹs.
-$$\mathbf { u } _ { 1 } = \left[ \begin{array} { r } 
2 \
- 4
\end{array} \right] , \mathbf { u } _ { 2 } = \left[ \begin{array} { r } 
12 \
6
\end{array} \right] , \mathbf { x } = \left[ \begin{array} { c } 
32 \
- 4
\end{array} \right]$$
A) $\mathbf { x } = 4 \mathbf { u } _ { 1 } + 2 \mathbf { u } _ { 2 }$
B) $\mathbf { x } = - 4 \mathbf { u } _ { 1 } - 2 \mathbf { u } _ { 2 }$
C) $\mathbf { x } = 2 \mathbf { u } _ { 1 } + 4 \mathbf { u } _ { 2 }$
D) $\mathbf { x } = 4 \mathbf { u } _ { 1 } - 2 \mathbf { u } _ { 2 }$

Quizplus · Accepted Answer

To express $\mathbf{x}$ as a linear combination of $\mathbf{u}_1$ and $\mathbf{u}_2$, we need to find scalars $a$ and $b$ such that $a\mathbf{u}_1 + b\mathbf{u}_2 = \mathbf{x}$. By substituting the given vectors into this equation and solving for $a$ and $b$, we find that $a = 4$ and $b = 2$ satisfy the equation, making $\mathbf{x} = 4\mathbf{u}_1 + 2\mathbf{u}_2$ the correct expression.

Express the Vector X as a Linear Combination of the Uʹs