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## Homework Statement

Prove that a set of linearly independent vectors in R

^{n}can have maximum n elements.

So how would you prove that the maximum number of independent vectors in R

^{n}is n?

I can understand why in my head but not sure how to give a mathematical proof. I understand it in terms of the number of independent vectors being equal to the rank of the matrix they create and obviously a matrix of dimension n can only have max n pivots. But I don't think that's really sufficient for a proof.

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