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Linear Algebra

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Easy

Zero Vector

LINALG-LUN9SL

Suppose that $V$ is a vector space. What must be true about $\vec 0$ in $V$?

A

$\vec v+\vec 0=\vec v$ for all $\vec v$ in $V$.

B

$\vec 0 +\vec v=\vec 0$ for all $\vec v$ in $V$.

C

$\vec 0+\vec v=\vec v$ for all $\vec v $ in $V$.

D

$\vec v+\vec 0=\vec v$ for some $\vec v$ in $V$. $\vec w+ \vec 0\neq \vec w$ for some $\vec w$ in $V$.

E

Choices 'A', 'C', 'D' are all correct.

F

Choices 'A' and 'C' are both correct.