WithN→∞ being fixed,R→∞, the free energy of the Matrix theory on a supergravity backgroundFis a functional ofF,W=W(R,F). We try to relate this functional withSeff(R,F), the effective action ofF, whereFis translation invariant alongx-. The vertex function is then associated with the connected correlation function of the current densities. FromW(R,F), one can construct an effective actionΓ(Y)for the arbitrary matrix configurationY.Γ(Y)isR,and thusp+independent. IfW(R,F)=Seff(R,F),Γ(Y)will give the supergravity interactions amongMtheory objects with no light-cone momentum exchange. We then discuss the Matrix theory dual of the11dbackground generated by branes with the definitep+as well as the gauge theory dual of the10dbackground arising from thex-reduction. Finally, for SYM4with the4dbackground fieldF0, we give a possible way to induce the radial dependent5dfieldF(σ).