Prove that a set of linearly independent vectors in Rn can have maximum n elements.
So how would you prove that the maximum number of independent vectors in Rn 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.