Can someone help me with this problem?
I have a $C^1$ function $G\colon\mathbb{R}^n\rightarrow \mathbb{R}^m$, where $k=n-m> 0$. If $M$ is the set of points $x\in G^{-1}(0)$ such that $(DG)_x$ has rank $m$, then $M$ is a smooth manifold of dimension $k$.
If someone could give me a starting kick it would be great!