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Zero element/unit element

  1. Sep 12, 2006 #1
    Let R^2 be a set containing all possible rows: (a b)

    when using the 8 axioms to prove whether (a,b) is indeed a vector space, i have to show that there is a zero element and a unit element.

    Is the zero element 0? or is it in matrix form such that W = (0 0) and W is contained in R^2?

    Is the unit element 1? or is it in matrix form such that F=(1 1) and F is contained in R^2?

    If I showed the 8 axioms are true, then does that show that R^2 is indeed a vector space?
  2. jcsd
  3. Sep 12, 2006 #2
    Your right about (0 0) and (1 1).
    And yes just show the 8 axioms hold.
    Last edited: Sep 12, 2006
  4. Sep 13, 2006 #3


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    Staff Emeritus
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    No, he's not right about (1, 1).

    indigojoker, you shouldn't even have to think about that. The "zero element" acts like 0: x+ 0= 0 in the VECTOR addition. If you are adding vectors the 0 has to be a vector: (0, 0). On the other hand, scalar multiplication involves multiplying a scalar by a vector: in "1v= v", the "1" is a number, not a vector.
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