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We consider the uplink of a multiuser system where the transmitters as well as the receiver are equipped with multiple antennas. Each user multiplexes its symbols by a linear precoder through its transmit antennas. We work with the system-wide mean squared error as the performance measure and propose algorithms to find the jointly optimum linear precoders at each transmitter and linear decoders at the receiver. We first work with the case where the number of symbols to be transmitted by each user is given. We then investigate how the symbol rate should be chosen for each user with optimum transmitters and receivers. The convergence analysis of the algorithms is given, and numerical evidence that supports the analysis is presented.