Let $F$ be a subspace over $\mathbb{R}$ or $\mathbb{C}$ (real or complex numbers), then determine whether the following is a subspace.
$\{ (x_{1}, x_{2}, x_{3}) \in F^{3} : x_{1}x_{2}x_{3} = 0\}$.
How do I check for closure under addition in this case?
Thanks in advance