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Homework Help: Proof of a theorem about spanning sets

  1. Mar 21, 2012 #1
    1. The problem statement, all variables and given/known data
    Let W be a subspace of R^n and let A be a subset of R^n. Then A spans W if and only if <A> = W (<A> is the set of all vectors in R^n that are dependent on A). Prove it.

    2. Relevant equations

    3. The attempt at a solution
    Ok the book goes likes this;
    First, it proves that if A spans W, then <A>=W
    It says that every vector in W is dependent on A, so W⊆<A>. But i do not get this part. Why is this true?
  2. jcsd
  3. Mar 21, 2012 #2
    Do you see it now?
  4. Mar 21, 2012 #3


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    Science Advisor

    What does "dependent on A" mean?
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