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# Space of Dimension $n$

LINALG-ISZDGL

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

Which of the following MUST be true?

Select ALL that apply.

A

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

B

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

C

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

D

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

E

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

F

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