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Subject: "What is wrong with this argument?? ..."     Previous Topic | Next Topic
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Mei Hee
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 Oct-22-00, 09:18 AM (EST)
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"What is wrong with this argument?? (Linear Algebra)"
 
   I am taking a Linear Algebra course recently. And I have been trying to prove that if a space V has a finite basis and W is the subspace of V, then there exists a finite basis for W. I wrote: "Let beta={v1, ..., vn} be a basis for V; then discard elements of beta one at a time until one gets a subset of beta which spans W." What is wrong with my argument???


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alexb
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672 posts		 Oct-22-00, 09:20 AM (EST)
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1. "RE: What is wrong with this argument?? (Linear Algebra)"
In response to message #0
 
   Take a 3d space and a 2d subspace - plane. Then find a basis in the space none of whose vectors belongs to the chosen plane.

In such a case, you will discard all the vectors of your basis beta without getting anything that is contained in the subspace,
let along spans it.

All the best,
Alexander Bogomolny


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