An optical-hybrid matrix processor is presented and compared in its speed with a digital electronic processor. Optical-hybrid matrix processors are shown to be far more superior in their speed in solving systems of linear equations. This advantage in speed increases with the increase of the matrix size. The problem of the convergence of the solution using the optical-hybrid is investigated. It is found that even with using elctro-optical systems with an error as high as 5% in the I/O devices, convergence was achieved for matrices with condition numbers as high as 150. Some means of improving the condition number of a matrix are also intoduced.