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Vector subspace as the space of solutions to matrix multiplication

  1. Feb 6, 2009 #1
    Given a subset W of a vector space V = F^n (for some field F), prove that W is the subspace of solutions of the matrix equation AX = 0 for some A.
     
  2. jcsd
  3. Feb 6, 2009 #2

    HallsofIvy

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    Why?

    Seriously, this sounds like a homework problem so it should be in the homework section.

    In any case, define the orthogonal complement of W and let A be the projection onto that complement.
     
  4. Feb 6, 2009 #3

    Hurkyl

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    I would just solve for A myself. :smile:
     
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