The edge-cloud system has the potential to combine the advantages of heterogeneous devices and truly realize ubiquitous computing. However, for service providers to guarantee the Service-Level-Agreement (SLA) priorities, the complex networked environment brings inherent challenges such as multi-resource heterogeneity, resource competition, and networked system dynamics. In this paper, we design a framework for the edge-cloud system, namely EdgeMatrix, to maximize the throughput while guaranteeing various SLA priorities. First, EdgeMatrix introduces Networked Multi-agent Actor-Critic (NMAC) algorithm to redefine physical resources as logically isolated resource combinations, i.e., resource cells. Then, we use a clustering algorithm to group the cells with similar characteristics into various sets, i.e., resource channels, for different channels can offer different SLA guarantees. Besides, we design a multi-task mechanism to solve the problem of joint service orchestration and request dispatch (JSORD) among edge-cloud clusters, significantly reducing the runtime than traditional methods. To ensure stability, EdgeMatrix adopts a two-time-scale framework, i.e., coordinating resources and services at the large time scale and dispatching requests at the small time scale. The real trace-based experimental results verify that EdgeMatrix can improve system throughput in complex networked environments, reduce SLA violations, and significantly reduce the runtime than traditional methods.