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Math Help - Algebra Proofs

  1. #1
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    Algebra Proofs

    Hi everyone,

    I am stuck on two problems, involving vector/matrix proofs: I think I would have to put these into a matrix of some sort, but I am unsure how to interpret it further. Some insight would be helpful

    Let Q= set{v1, v2, ..., vq} in r^n

    1. Prove that if n<q, then there exists a vector in R^n that is not in the element of Span Q..

    2. Prove that if n>q, then Q is linearly independent.

    THanks!
    Last edited by KelvinScc; January 27th 2011 at 06:02 PM.
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  2. #2
    MHF Contributor

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    What you've written makes no sense. You say "if k< q" but there is NO "k" in the "let Q= ..." part. Did you mean
    "Let Q= set{v1, v2, ..., vq} in R^k?"

    If so, then you will need to use the fact that R^k has dimension k.
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  3. #3
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    Sorry, I meant if q<n and q>n.
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