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jumbogala
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Homework Statement
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.
Homework Equations
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?