We consider relay broadcast channels (RBCs) with multiple antennas at all nodes. A practical linear preceding, relaying and combining scheme is proposed. Under an overall power constraint, we derive the optimal power allocation solution in a closed form. A low complexity beamforming vector optimization algorithm is proposed to maximize the effective channel gains and improve the system performance. Simulation results are presented for various channel configurations, which show that the proposed optimized beamforming algorithm achieves performance very close to that of the exhaustive search algorithm but with a much lower complexity, and the maximum diversity gain is always attained.