We show that over any field, the solution set to a system of n linear equations in n unknowns can be computed in parallel with randomization simultaneously in poly-logarithmic time in n and with only as many processors as are utilized to multiply two n×n matrices. A time unit represents an arithmetic operation in the field. For singular systems our parallel timings are asymptotically as fast as those for non-singular systems, due to our avoidance of binary search in the matrix rank problem,

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... pt when the field has small positive characteristic; in that case, binary search is avoided at a somewhat higher processor count measure.