  We consider the electron magnetohydrodynamics (MHD) equation on the 3D torus
$\mathbb T^3$. For a given smooth vector field $H$ with zero mean and zero
divergence, we can construct a weak solution $B$ to the electron MHD in the
space $L^\gamma_tW^{1,p}_x$ for appropriate $(\gamma, p)$ such that $B$ is
arbitrarily close to $H$ in this space. The parameters $\gamma$ and $p$ depend
on the resistivity. As a consequence, non-uniqueness of weak solutions is
obtained for the electron MHD with hyper-resistivity. In particular,
non-Leray-Hopf solutions can be constructed. As a byproduct, we also show the
existence of weak solutions to the electron MHD without resistivity.
