Upgrade to access all content for this subject

Suppose that $V$ is a vector space of dimension $n$.

Which of the following MUST be true?

Select ALL that apply.

$V$ must be the vector space $R^n$.

Every basis for $V$ must contain exactly $n$ elements.

Every set of $n$ linearly independent elements of $V$ is a basis for $V$.

Every set of elements that spans $V$ has exactly $n$ elements.

Every set of elements of $V$ which contains more than $n$ elements is linearly dependent.

No set of elements of $V$ which contains less than $n$ elements is linearly dependent.