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Subsets and subspaces of vector spaces

  1. Nov 10, 2009 #1
    1. The problem statement, all variables and given/known data

    T = {(1,1,1),(0,0,1)} is a subset of R[tex]^{3}[/tex] but not a subspace

    sol

    i have to prove it holds for addition and scalar multiplication

    so let x=(1,1,1) and y =(0,0,1) so x+y = (1,1,2)

    so it holds

    let [tex]\alpha[/tex] = a scalar
    then [tex]\alpha[/tex]x = ([tex]\alpha[/tex],[tex]\alpha[/tex],[tex]\alpha[/tex])
    and [tex]\alpha[/tex]y = (0,0,[tex]\alpha[/tex])

    so that holds.

    i think i've shown that it is a subpace but the question says it isnt?
     
    Last edited: Nov 10, 2009
  2. jcsd
  3. Nov 10, 2009 #2

    Mark44

    Staff: Mentor

    Re: suspace

    I don't think you have given us the exact wording of this problem. The two vectors you gave are a basis for and span a two-dimension subspace of R^3.
     
  4. Nov 10, 2009 #3

    Mark44

    Staff: Mentor

    Re: suspace

    Thinking about this some more, you have a set T with two vectors in it. With x and y as before, is x + y in the set? Is cx in the set for an arbitrary scalar?
     
  5. Nov 10, 2009 #4
    Re: suspace

    i think they are in the set, x+y = (1,1,2) which is in R^3 and cx= (c,c,c) which is also in R^3 for any scalar c
     
  6. Nov 10, 2009 #5

    Mark44

    Staff: Mentor

    Re: suspace

    The set T is {(1, 1, 1), (0, 0, 1)}. How can you say that x + y is in this set? If c = 2, is c(1, 1, 1) in this set?
     
  7. Nov 10, 2009 #6
    Re: subspace

    am i not just to show that they are in R^3?
     
  8. Nov 10, 2009 #7

    Mark44

    Staff: Mentor

    Re: suspace

    Do you know the definition of a subspace of a vector space?
     
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