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Vector space

  1. Oct 7, 2007 #1
    15. Determine wheter the set is a vector space.
    The set of all fifth-degree polynomials with the standard operations.
    AXIOMS
    1.u+v is in V
    2.u+v=v+u
    3.u+(v+w)=(u+v)+w
    4.u+0=u
    5.u+(-u)=0
    6. cu is in V
    7.c(u+v)=cu+cv
    8.(c+d)u=cu+cd
    9.c(du)=(cd)u
    10.1(u)=u

    the axioms that fail are 1,4,5, and 6. I dont know why 4,5,and 6 fail. Can anyone help me?
     
  2. jcsd
  3. Oct 8, 2007 #2

    Gokul43201

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    Staff Emeritus
    Science Advisor
    Gold Member

    How is the degree of a polynomial defined? Now, what is the additive identity, and is it a fifth-degree polynomial?
     
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