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Homework Help: Prove that a set cannot be expressed as a linear span

  1. Oct 6, 2012 #1
    1. The problem statement, all variables and given/known data
    Can these sets be expressed as a linear span? Justify your answers.
    (i) [itex]A = \{ (x,2x + y,3y,y - 2)|x,y,z \in ℝ\} [/itex]
    (ii) [itex]B = \{ (x,y,z)|y = {z^2}\} [/itex]
    (iii) [itex]C = \{ (a,b,c,d)|a \ne b[/itex] and [itex]c \ne d\} [/itex]

    2. Relevant equations

    3. The attempt at a solution
    Actually I have no problem writing down A as a linear span. Intuitively, I guess B and C are not linear spans but I don't know how to prove it. Any hint is greatly appreciated, thanks!
  2. jcsd
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