Show that this system is not a vector space

  1. 1. The problem statement, all variables and given/known data

    Show that the system S is not a vector space by showing one of the axioms is not satisfied with the usual rules for addition and multiplication by a scalar in ℝ3

    S={x(ℝ3):2x1+3x32-4x23=0}


    2. Relevant equations



    3. The attempt at a solution

    The subscripts for the x's are strange I think but I guess that shouldn't make a difference.

    But I'm really stuck on this I think it should be fairly easy though.

    but for example if I try closure under scalar multiplication

    or closure under addition I keep coming to a dead end because I don't know the value of the x's.

    ie λ[2x1+3x32-4x23]=λ[0]

    ...λ[2x1+3x32-4x23]=0

    I think I just need a hint in the right direction. Thanks
     
  2. jcsd
  3. HallsofIvy

    HallsofIvy 40,689
    Staff Emeritus
    Science Advisor

    The way I see it, you have one major problem- what you are trying to prove is not true!

    Now, please tell us the exact wording of the problem. I suspect you are misstating it.
     
  4. Mark44

    Staff: Mentor

    I don't understand what you have above. Presumably x is a vector in R3. Why are there two subscripts on some of the variables in your equation?
     
  5. Ok sorry I did mistake the problem.

    it really should have said 2x1+3x32-4x32

    I mistakenly read it as it was not typed out ver well and it appeared to look like weird subscript notation.

    and I solved it no problems

    Thanks for letting me know!
     
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