This paper investigates transmit antenna selection for linearly precoded multiuser multiple-input-multiple-output (MU-MIMO) systems. First, in some precoded single-user MIMO systems, using all transmit antennas does not always lead to the best performance due to ill-conditioned channel matrices. This condition motivates us to investigate whether a similar result can be obtained in MU-MIMO systems. Based on the derived analytical results, we found that, for a given number of transmit antennas, decreasing the number of active transmit antennas [number of radio frequency (RF) units] always degrades system performance in the linearly precoded MU-MIMO systems. However, in practical systems, RF units are expensive. To reduce the hardware cost, antenna selection is usually used to reduce the number of RF units. Thus, we further analyze the performance loss due to transmit antenna selection (TAS). These analytical results provide good design references for using TAS in practical systems. Moreover, based on the analytical results, we proposed several simple TAS algorithms for linearly precoded MU-MIMO systems. Complexity analysis and simulation results show that the computational complexity of the proposed algorithms can significantly be reduced, whereas the performance is still comparable with the optimal selection scheme. As a result, the analyzed results enable us to better understand how TAS affects the MU-MIMO systems. In addition, the proposed algorithms make TAS more feasible to be used in practical systems.