The paper is in the scope of studies on the rf driving of a matrix source of negative hydrogen ions: a matrix of small radius discharges with planar-coil inductive driving and single aperture extraction from each discharge. The results from a three-dimensional model, in which plasma description is coupled to electrodynamics, confirm former conclusion that a single coil driving of the whole matrix by a zigzag coil with an omega-shaped conductor on the bottom of each discharge tube ensures efficient rf power deposition to the plasma. The latter is due to similarities with the rf driving of a single discharge by a single planar coil, shown by the obtained induced current and spatial distribution of the plasma parameters. Distinctions associated with the coil configuration as a single coil for the whole matrix are also discussed.