Upgrade subject to access all content

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.

$S=V$

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

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

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

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

None of the above.