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Homework Help: Solution space and subspace

  1. May 19, 2007 #1
    1. The problem statement, all variables and given/known data

    Let A =

    [2 -1 9]
    [1 0 5]
    [0 1 1]

    Find solution space W and prove that W is a subspace of R^3.

    2. Relevant equations

    3. The attempt at a solution

    [1 0 5]
    [0 1 1]
    [0 0 0]

    So I know the row-echeleon form, which is what I suppose is the solution space. But how do you prove that it's a subspace of R^3? Using the vector space axioms? How do you use those on this kind of matrix?
  2. jcsd
  3. May 20, 2007 #2


    User Avatar
    Staff Emeritus
    Science Advisor

    The matrix isn't the solution space. The solution space is the set of vectors x such that Ax=0.
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