$$\{(x,y,z)|2x+9y=0, 8x-5z=0\}$$
I solved these as simultaneous equations giving me the equation $36y + 5z = 0$ or $y=-\frac{5}{36}z$, which I can write as
$$ \begin{bmatrix} -\frac{5}{36}z \\ z \\ \end{bmatrix} = 0.$$
Substituting $0$ for $z$ satisfies this equation. And it is closed multiplication and addition so this the original set is a subspace of $\mathbb{R}^3$. Is that method correct or am I completely off with this?