With N → ∞ being fixed, R → ∞ , the free energy of the Matrix theory on a supergravity background F is a functional of F , W = W ( R , F ) . We try to relate this functional with S eff ( R , F ) , the effective action of F , where F is translation invariant along x - . The vertex function is then associated with the connected correlation function of the current densities. From W ( R , F ) , one can construct an effective action Γ ( Y ) for the arbitrary matrix configuration Y . Γ ( Y ) is R, and thus p + independent. If W ( R , F ) = S eff ( R , F ) , Γ ( Y ) will give the supergravity interactions among M theory objects with no light-cone momentum exchange. We then discuss the Matrix theory dual of the 11 d background generated by branes with the definite p + as well as the gauge theory dual of the 10 d background arising from the x - reduction. Finally, for SYM ₄ with the 4 d background field F 0 , we give a possible way to induce the radial dependent 5 d field F ( σ ) .