Is the solution set of Ax ≥ B convex set in different situation

Question

$\Omega_1:\{x\in R^n|Ax=b,x\ge0 \}$
$\Omega_2:\{x\in R^n|Ax\ge b\}$,$A$ is full row rank matrix.
$\Omega_3:\{x\in R^n|Ax\ge b\}$,$A$ is full column rank matrix.
Provided $\Omega_1,\Omega_2,\Omega_3 $ are not empty,then which set is to (must) have extreme point?
I consider that I could prove it by proving the set to be convex set, but I have no idea how to do that.