Question

If v is of dimension n, show that any set of n linearly independent vectors in v forms a basis of v
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Answer 1

Answer:

There is nothing to prove since the dimension of V is n and the fact that any set of n linearly independent vectors form a basis is immediately true by the definition of basis.

Notably note that any set of n linearly independent vectors span V, indeed since V has a basis of n vectors if the new set didn't span V we would have a contradiction.

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