Reconfigurable Intelligent Surfaces (RIS) can intelligently manipulate wireless channels to provide auxiliary transmission paths for communication systems. However, due to the "multiplicative fading" effect inherent in passive RIS (PRIS), existing PRIS-assisted hybrid cooperative systems can only achieve limited capacity gains in scenarios with weak direct links. To overcome this limitation, this paper introduces active RIS (ARIS) technology, leveraging its advantages such as flexible active beamforming and signal control, relatively low overall power consumption, and cost-effectiveness. Considering the stable reliability and widespread deployment of traditional relays, we investigate a hybrid system integrating ARIS with decode-and-forward (DF) relay in a multiple-input multiple-output (MIMO) framework. To maximize the system’s achievable rate, we formulate a joint optimization problem involving the source transmit beamforming matrix, relay transmit beamforming matrix, and ARIS active beamforming matrix. A joint optimization algorithm based on alternating optimization (AO) and fractional programming (FP) is proposed, decoupling the original problem into multiple standard quadratically constrained quadratic programming (QCQP) subproblems, which are then solved using the Lagrangian multiplier method. Simulation results demonstrate that the proposed system significantly outperforms benchmark schemes, with performance advantages becoming more pronounced as the number of RIS reflective elements increases.