Nondegeneracy of the Lie algebra aff(n)

We show that $\mathfrak{a}\mathfrak{f}\mathfrak{f}(n)$, the Lie algebra of affine transformations of ${\mathbb{R}}^n,$ is formally and analytically nondegenerate in the sense of A. Weinstein. This means that every analytic (resp., formal) Poisson structure vanishing at a point with a linear part corresponding to $\mathfrak{a}\mathfrak{f}\mathfrak{f}(n)$ is locally analytically (resp., formally) linearizable.