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Linear Algebra and Matrices, Subspaces, basis

  1. Nov 9, 2008 #1
    1. The problem statement, all variables and given/known data

    I'm unclear about this statement being wrong or not:
    if C is an x-dimensional subspace of Rn, then a linearly independent set of x vectors in C is a basis for C

    3. The attempt at a solution

    I think that it must be a basis since it has independent vectors and it is in x dimensions, so there are x vectors in it. What I'm not so sure about is whether or not if it spans the subspace, but I think it does since all the vectors are independent, so there are x of them, so it should span in x dimensions.

    I also want to thank HallsofIvy for lots of help with me with the questions 2 days ago.
     
  2. jcsd
  3. Nov 9, 2008 #2

    Dick

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    Sure it's right. Isn't that the definition of dimension? The number of independent vectors required to span C?
     
  4. Nov 9, 2008 #3

    HallsofIvy

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    If V is a vector space of dimension N, then a basis for V has three properties:
    1) The vectors in the basis are independent.
    2) The vectors span V.
    3) There are N vectors in the basis.

    If any two of those are true, the third is also.
     
  5. Nov 9, 2008 #4
    Thanks you two. :)
     
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