The span of $a$ and $b$ is the set of linear combinations of the vectors $a$ and $b$. This isn't too hard to write down here; no need to reduce, the vectors have disjoint support. The span is all vectors of the form $$\alpha(0,3,-2)+\beta(1,0,0)=(\beta, 3\alpha,-2\alpha)$$ where $\alpha$ and $\beta$ are scalars.
In particular, taking $\alpha=1=\beta$ shows that $(1,3-2)$ is in the span. For any values of $\alpha$ and $\beta$, you have an element in the span.
In fact, the span is a two dimensional subspace of $\Bbb R^3$; so
you could describe the span of $a$ and $b$ geometrically as a certain plane. Namely, the plane through the origin in $\Bbb R^3$ that contains both the vectors $a$ and $b$.