# Explanation regarding statement of the Implicit Function Theorem .

My notes define the implicit function theorem as follows :

Let $E$ be an open set in $\mathbb R^{n+m}$ and $f\in C^1(E,\mathbb R^n)$ such that for some $f(a,b)=0$ for some $(a,b)\in E$ .
Let $A$ be the jacobian of $f$ at $(a,b)$. Then $A$ is an $n+m\times n$ matrix.
Write $A=[A_1~~ A_2]$ . Assume that $A_1$ is invertible.