We address the problem of designing linear precoder and decoder for single symbol transmission in three node amplify-and-forward (AF) multi-input-multi- output (MIMO) relay systems where all the nodes are equipped with multiple antennas and the source and the relay nodes are subject to individual transmit power constraints. We first find the optimal decoder to maximize the average received signal-to-noise- ratio (SNR). Next, the source and the relay precoders are designed for maximizing a lower bound on the total SNR. Further, a decision criterion as to whether the relay node should participate in transmission is derived. Simulation results show significant improvement in the received SNR and bit error rate (BER) by applying the proposed precoding and decoding schemes. It is also shown that the computational complexity of the proposed scheme is much lower than other methods in the literature.