  We extend the quantum Hall matrix model to include couplings to external
electric and magnetic fields. The associated current suffers from matrix
ordering ambiguities even at the classical level. We calculate the linear
response at low momenta -- this is unambigously defined. In particular, we
obtain the correct fractional quantum Hall conductivity, and the expected
density modulations in response to a weak and slowly varying magnetic field.
These results show that the classical quantum Hall matrix models describe
important aspects of the dynamics of electrons in the lowest Landau level. In
the quantum theory the ordering ambiguities are more severe; we discuss
possible strategies, but we have not been able to construct a good density
operator, satisfying the pertinent lowest Landau level commutator algebra.
