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Proving real vector spaces

  1. Sep 13, 2011 #1
    1. The problem statement, all variables and given/known data

    Show whether the set is a vector space: The set of all triples of real numbers (x, y, z) with the operations:

    (x, y, z) + (x', y', z') = (x + x', y + y', z + z') and k(x, y, z) = (kx, y, z)

    2. Relevant equations

    (10 vector space axioms)

    3. The attempt at a solution

    I can understand 9 axioms, I just want to confirm that I am doing the right thing on this one:

    (m + k)(x, y, z) = ((m+k)x, y, z), which is not equal to k(x, y, z) + m(x, y, z) = (kx, y, z) + (mx, y, z) = ((m+k)x, 2y, 2z).

    Is this correct working?

    Thanks

    Derryck
     
  2. jcsd
  3. Sep 13, 2011 #2

    vela

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    Yup.
     
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