I've tried to solve this:

Suppose there is a linear system which S is the solution set of it, $\displaystyle 0\in \mathbb{R}$ therefore $\displaystyle \left ( 0,0,0 \right ) \in S=\left \{ \left ( a,a^2,b \right )|a,b\in \mathbb{R} \right \}$.

So, now I can tell that this is homogeneous systems.

I'll show the contradiction,

$\displaystyle \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. $\displaystyle -1 \in \mathbb{R}$ and

But $\displaystyle \forall a \in \mathbb{R}\rightarrow a^2\neq -x_2$.

therfore , and $\displaystyle S$ is not the solution set.

What do you think about my answer?