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Linear Algebra

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Moderate

Visualizing Vector Operation: Inverses and Non-Standard Position

LINALG-LHFXGY

Let $\boldsymbol{v}$ be a vector in $\mathbb{R}^2$ whose tail is positioned in the first quadrant and whose head is positioned in the third quadrant. In which quadrant does the vector $-4\boldsymbol{v}$ terminate, if $-4\boldsymbol{v}$ is expressed in standard position?

A

First quadrant.

B

Second quadrant.

C

Third quadrant.

D

Fourth quadrant.

E

Cannot be determined from this information.