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Homework Help: Vector space prove 0u=0

  1. Mar 24, 2012 #1
    1. The problem statement, all variables and given/known data
    prove 0u=0 where u is in the vector space.

    2. Relevant equations
    the 10 various axioms for addition and scalar multiplication.

    3. The attempt at a solution
    pretty much just


    and then i get stuck. i can prove that -1u=-u but that involves 0u-0
  2. jcsd
  3. Mar 24, 2012 #2
    Couldn't you let u = (a,b), then
  4. Mar 24, 2012 #3
    No, Bearded Man. You made an assumption about "what vectors are" that doesn't follow from the axioms. Some vector spaces are described by components, but not all, and it's certainly not necessarily two-dimensional.

    Try this:

    Distribute, and see where it takes you.
  5. Mar 25, 2012 #4
    Here you go Brandy:

    0 x u = 0 + 0 x u
    = -u + u + 0 x u
    = -u + (1 + 0) x u
    = -u + 1 x u
    = -u + u
    = 0

    And maybe you can help me with this one.
    v + x = w + x
    Prove v = w
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