Basis proof

  • Thread starter eyehategod
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  • #1
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Let S be a linearly independent set of vectors from the finite dimensional vector space V.
Prove that there exists a basis for V containing S.

How do I start this proof?
I wasn't able to get it on my test.
 

Answers and Replies

  • #2
Dick
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If S doesn't span V, then pick a vector s1 that's not in the span of S. Let S1={s1}US. Show S1 is linearly independent. If S1 doesn't span V, repeat the process and get S2. Etc. Since dim(V) is finite this has to stop somewhere.
 
  • #3
HallsofIvy
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You can also, by the way, prove this for an infinite dimensional vector space but the proof is much harder!
 

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