If V is a vector space with finitely many elements, what can you say about the number of elements in V?
Does the answer have anything to do the with dimension of the basis for the vector space?
2026-03-31 21:17:27.1774991847
If V is a vector space with finitely many elements, what can you say about the number of elements in V?
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I'm assuming you mean real vector space (meaning a vector space over the real numbers $\mathbb{R}$), since more generally a vector space is an object associated with a particular field.
Assuming this is the case, suppose you have a vector $v$ from your finite vector space $V$. Are there any other vectors that you know must be in $V$? How many of them are there? Is it possible that $V$ is empty?