1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?



Similar Discussions: Prove that a set cannot be expressed as a linear span
Loading...