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Proving something is a vector space

  1. Oct 16, 2014 #1
    1. The problem statement, all variables and given/known data
    Consider the set V = R^2 (two dimensions of real numbers) with the following operations of vector addition and scalar multiplication:

    (x,y) + (z,w) = (x+y-1, y+z)
    a(x,y) = (ax-a+1,ay)

    Show that V is a vector space

    2. Relevant equations
    None

    3. The attempt at a solution
    So the first axiom of a vector space is showing that the scalar addition is commutative. However, to me it seems like given the wonky definition of vector addition it is not commutative.

    (x,y) + (z,w) = (x+y-1, y+z)
    (z,w) + (x,y) = (z+w-1, w+x)

    These are only equal to each other if x=z and y=w. Do ya'll think this is a typo?
     
  2. jcsd
  3. Oct 16, 2014 #2

    vela

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    Yeah, I think it's a typo. You should check with your professor.
     
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