The Yvon-Born-Green, Kirkwood and Kirkwood-Salsburg integral equation hierarchies have been obtained for the case of a fluid adsorbed into a host medium made up of immobile particles. Despite earlier work which showed that the Ornstein-Zernicke equations for this situation were fundamentally different from those of a binary equilibrium fluid mixture, the pure-fluid and mixed-fluid-matrix Yvon-Born-Green and Kirkwood-Salsburg equations for the matrix-averaged distribution functions, g(f)((n)) and for g(mf)((n)), are found to be identical to those for the equilibrium mixture. However, the equilibrium mixture equations for g(m)((n)) do not apply. At present, the Kirkwood equation does not appear in a matrix-averaged form suitable for numerical work. The Kirkwood-Salsburg equations can be used to generate the fundamental graph theory for the problem. In practical calculations, the special role of the matrix enters principally in the closures used to truncate the hierarchy of equations. The standard Kirkwood superposition approximation is appropriate in this application, and circumstances in which practical corrections to the superposition approximation can be employed are considered.