Background independent effective action from D = 1 matrix model

We derive the background independent from of the Das-Jevicki action. The tachyon terms are given to all orders by a generally covariant form of the Das-Jevicki action. The graviton-dilaton sector is the usual low energy effective action. This enables us to examine questions such as the back reaction of the tachyon on the metric. In particular the reason why the usual Liouville term is an exact solution of the conformal invariance conditions, as well as the fact that it has no back reaction, become manifest. We comment on the propagation of a tachyonic perturbation in the background of a black-hole metric.