  We present a finite dimensional matrix model associated to the noncommutative
Chern-Simons theory, obtained by inserting a Wilson line. For a specific choice
of the representation of the Wilson line the model is equivalent to the minimal
modification of the matrix model which is compatible with finite dimensional
matrices, and was introduced previously to study droplets of quantum Hall
fluid. For other representations we obtain generalizations corresponding to
regularized U(n) Chern-Simons theoris, representing multilayered quantum Hall
fluids.
