The question:

Show that the set

$\displaystyle S = \{x \in \mathbb{R}^3 : x_1 \le 0, x_2 \ge 0 \}$

with the usual rules for addition and multiplication by a scalar in $\displaystyle \mathbb{R}^3$ is not a vector space by showing that at least one of the vector-space axioms is not satisfied. Give a geometric interpretation of this result.

My attempt:

There's no solution to this answer in my text. My understanding is that this set is not closed under scalar multiplication, since multiplying by -1 will reverse the conditions on $\displaystyle x_1$ and $\displaystyle x_2$. Is this correct?

As for the second part of the question, it asks for a geometric interpretation, which I'm not sure about. It's a 3D object, but otherwise I don't know how else to interpret it. Any ideas?

Thanks.