Let $\displaystyle A$ be a symmetric $\displaystyle n \times n$ matrix over $\displaystyle \mathbb{R}$.

Let $\displaystyle 0 \neq b \in \mathbb{R}$.

Show that the surface $\displaystyle M = \{x\in \mathbb{R}^n \mid x^T A x = b\}$ is an $\displaystyle (n - 1)$ dimensional submanifold of the manifold $\displaystyle \mathbb{R}^n$.

Please, help!