  The effective action for the membrane dynamics on the background geometry of
the $N$-sector DLCQ $M$ theory compactified on a two-torus is computed via
supergravity. We compare it to the effective action obtained from the matrix
theory, i.e., the (2+1)-dimensional supersymmetric Yang-Mills (SYM) theory,
including the one-loop perturbative and full non-perturbative instanton
effects. Consistent with the DLCQ prescription of $M$ theory {\em a la}
Susskind, we find the precise agreement for the finite $N$-sector
(off-conformal regime), as well as for the large $N$ limit (conformal regime),
providing us with a concrete example of the correspondence between the matrix
theory and the DLCQ $M$ theory. Non-perturbative instanton effects in the SYM
theory conspire to yield the eleven-dimensionally covariant effective action.
