# Prove that a set cannot be expressed as a linear span

1. Oct 6, 2012

### drawar

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

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!