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Basis proof

  1. Dec 13, 2007 #1
    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.
     
  2. jcsd
  3. Dec 13, 2007 #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.
     
  4. Dec 13, 2007 #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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