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Linear Algebra

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Moderate

Spanning Sets - $A$, $B$ and Their Spans

LINALG-VFL1VX

Suppose that $A, B$ are nonempty sets of vectors in some vector space $V$. Which of the following are true?

Select ALL that apply.

A

The span of $A\cap B$ is a subset of the span of $A\cup B$.

B

$\vec 0$ is element of both the span of $A$ and the span of $B$.

C

If the $A\cap B$ is the empty set, then the span of $A$ and the span of $B$ have no elements in common other than $\vec 0$.