The cooperative output regulation problem of linear heterogeneous multi-agent systems by a distributed observer has been solved under the assumption that the control of each follower knows the system matrix of the leader system. In this paper, we will solve the same problem by removing this assumption by making use of the adaptive distributed observer proposed recently. This adaptive distributed observer will provide, to each follower, not only the estimation of the leader's signal, but also the estimation of the leader's system matrix. Thus, based on the estimation of the system matrix of the leader system, we will devise an adaptive algorithm to calculate the solution of the regulator equations associated with each follower, and obtain an estimated feedforward gain. The estimated leader's signal and the estimated feedforward gain will further lead to an adaptive distributed control law to solving the problem.