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Linear Algebra

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Spans of $A$ and $B$

LINALG-N1EGOX

Suppose that $A,B$ are subsets of a vector space $V$ and that the span of $A$ is a proper subset of the span of $B$.

Which of the following are POSSIBLE?

Select ALL that apply.

A

$A$ is a subset of $B$.

B

$B$ is a subset of $A$.

C

$A=B$

D

$A\cap B=\emptyset$

E

$A$ is not a subset of $B$ nor is $B$ a subset of $A$. However, $A\cap B\neq \emptyset$.