Find the vector $\mathbf { z }$, given $\mathbf { u } = \langle - 4,9,8 \rangle , \mathbf { v } = \langle 5,4,4 \rangle$, and $\mathbf { w } = \langle - 3,23,4 \rangle$. $3 \mathbf { u } - \mathbf { v } + 2 \mathbf { z } = \mathbf { w }$
A) $\langle 14,0 , - 16 \rangle$
B) $\langle 0,7 , - 8 \rangle$
C) $\langle - 7,0 , - 8 \rangle$
D) $\langle 7,0 , - 8 \rangle$
E) $\langle 8,0 , - 7 \rangle$

Question

Quizplus · Accepted Answer

To find $\mathbf{z}$, we first calculate $3\mathbf{u} - \mathbf{v}$ and then solve for $\mathbf{z}$ in the equation $3\mathbf{u} - \mathbf{v} + 2\mathbf{z} = \mathbf{w}$. Calculating $3\mathbf{u} - \mathbf{v}$ gives us $\langle -12,27,24 \rangle - \langle 5,4,4 \rangle = \langle -17,23,20 \rangle$. Substituting into the equation and solving for $\mathbf{z}$ gives us $\mathbf{z} = \langle 7,0,-8 \rangle$.

Find the Vector z\mathbf { z }z , Given u=⟨−4,9,8⟩,v=⟨5,4,4⟩\mathbf { u } = \langle - 4,9,8 \rangle , \mathbf { v } = \langle 5,4,4 \rangleu=⟨−4,9,8⟩,v=⟨5,4,4⟩

Find the Vector $\mathbf { z }$ , Given $\mathbf { u } = \langle - 4,9,8 \rangle , \mathbf { v } = \langle 5,4,4 \rangle$