  We develop a supersymmetric extension of the Susskind-Polychronakos matrix
theory for the quantum Hall fluids. This is done by considering a system
combining two sets of different particles and using both a component field
method as well as world line superfields. Our construction yields a class of
models for fractional quantum Hall systems with two phases U and D involving,
respectively $N_1$ bosons and $N_2$ fermions. We build the corresponding
supersymmetric matrix action, derive and solve the supersymmetric
generalization of the Susskind-Polychronakos constraint equations. We show that
the general U(N) gauge invariant solution for the ground state involves two
configurations parameterized by the bosonic contribution $k_{1}$ (integer) and
in addition a new degree of freedom $k_{2}$, which is restricted to 0 and 1. We
study in detail the two particular values of $k_{2}$ and show that the
classical (Susskind) filling factor $\nu $ receives no quantum correction. We
conclude that the Polychronakos effect is exactly compensated by the opposite
fermionic contributions.
