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HallsofIvy
#4
Jan8-11, 11:32 AM
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Linearly Independent Sets and Bases

Quote Quote by JonF View Post
I would show that any S could be extended to be a basis for V, then show that a basis for V can be extended to be a basis for Rn.
Sorry, but this makes no sense to me. The problem was to show that any such S could be extended to a basis for V and there is no mention of Rn.

Let B be a basis for S, what would the minimal subset of B look like that spans V?
This also makes no sense. S is a set of vectors, not a vector space and so has no "basis". Even if S were a subspace of V, any basis for V would have to be a superset of a basis for S, not a subset.

Ask your self a similar question to go from V to Rn
Unnecessary- the problem says nothing about Rn.