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Linear Algebra

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Moderate

Span of $S$ is $V$

LINALG-ZO4EMN

Suppose that $S$ is a set of vectors in a vector space $V$, and that the span of $S$ is equal to $V$.

Which of the following MUST be true?

Select ALL that apply.

A

$S=V$

B

The elements of $S$ form a basis for $V$.

C

A subset of the elements of $S$ form a basis for $V$.

D

A proper subset of the elements of $S$ form a basis for $V$.

E

Every element in $V$ can be expressed as a linear combination of elements in $S$.

F

None of the above.