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# Visualizing Vector Operations: Lattices and Linear Combinations

LINALG-VMRQXB

The vectors $\boldsymbol{u}$, $\boldsymbol{v}$, and $\boldsymbol{w}$ in $\mathbb{R}^2$ are illustrated below. Which of the following linear combinations of $\boldsymbol{u}$ and $\boldsymbol{v}$ are equal to $\boldsymbol{w}$?

A

$\boldsymbol{u} - 2\boldsymbol{v}$

B

$3\boldsymbol{u} + 2\boldsymbol{v}$

C

$2\boldsymbol{u} - 3\boldsymbol{v}$

D

$2\boldsymbol{u} - \boldsymbol{v}$

E

$2\boldsymbol{u} - \boldsymbol{v}$

F

$3\boldsymbol{u} - 2\boldsymbol{v}$

G

$\boldsymbol{u} + \boldsymbol{v}$

H

$\boldsymbol{u} - 3\boldsymbol{v}$