Find the vector $\mathbf { z }$, given $\mathbf { u } = \langle 0 , - 8 , - 4 \rangle , \mathbf { v } = \langle - 5,0 , - 6 \rangle$, and $\mathbf { w } = \langle - 17,25 , - 1 \rangle$. $- 2 \mathbf { u } + 4 \mathbf { v } - 3 \mathbf { z } = \mathbf { w }$
A) $\langle 3,9,15 \rangle$
B) $\langle - 3 , - 1 , - 5 \rangle$
C) $\langle 1,3 , - 5 \rangle$
D) $\langle - 1 , - 3 , - 5 \rangle$
E) $\langle 0 , - 3 , - 4 \rangle$

Question

Quizplus · Accepted Answer

First, calculate $-2\mathbf{u} + 4\mathbf{v}$ which equals $\langle -20, 16, -24 \rangle$. Then, rearrange the equation to solve for $\mathbf{z}$ by subtracting the result from $\mathbf{w}$, giving $\mathbf{z} = \frac{\mathbf{w} - (-2\mathbf{u} + 4\mathbf{v})}{-3}$. Substituting the values gives $\mathbf{z} = \langle -1, -3, -5 \rangle$.

Find the Vector z\mathbf { z }z , Given u=⟨0,−8,−4⟩,v=⟨−5,0,−6⟩\mathbf { u } = \langle 0 , - 8 , - 4 \rangle , \mathbf { v } = \langle - 5,0 , - 6 \rangleu=⟨0,−8,−4⟩,v=⟨−5,0,−6⟩

Find the Vector $\mathbf { z }$ , Given $\mathbf { u } = \langle 0 , - 8 , - 4 \rangle , \mathbf { v } = \langle - 5,0 , - 6 \rangle$