## Re: proof of no existence of liner system over R

I've tried to solve this:
Suppose there is a linear system which S is the solution set of it, $0\in \mathbb{R}$ therefore $\left ( 0,0,0 \right ) \in S=\left \{ \left ( a,a^2,b \right )|a,b\in \mathbb{R} \right \}$.
So, now I can tell that this is homogeneous systems.
$\left ( x_1,x_2,x_3 \right )\in S$ so the linear system is homogeneous, so scalar multiplication is also a solution to the system. $-1 \in \mathbb{R}$ and
But $\forall a \in \mathbb{R}\rightarrow a^2\neq -x_2$.
therfore , and $S$ is not the solution set.