(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Among all independent vector sets in a vector space U, let M = {v1, v2, ... vp} be an independent set. p is as large as it can get. Show that U is a basis of M.

2. Relevant equations

3. The attempt at a solution

If U is a basis of M then U is an independent set (we already know it is) and U spans M.

Or, since the dimension is the maximum number of linearly independent vectors you can have in a subset, if dim(U) = the number of elements in M, then it is a basis.

dim(U) = p, since p is as big as it can get

and there are p elements in M so it's a basis.

That seems too simple though. Plus it doesn't show that U spans M, which I think is probably necessary. Can anyone help?

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# Homework Help: Showing that something is a basis of an independent set

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