Solution of simultaneous equations by block elimination

THIS paper presents an exact method for solving simultaneous linear algebraic equations which the author believes has many advantages over other procedures. It extends the familiar method of eliminating a single unknown at a time to that of eliminating large groups in a single process. A close relationship to the reduction or “partitioning” of matrices1,2 is also seen to exist. The process is applicable to small sets of equations to be solved by hand or keyboard as well as to larger sets to be solved by digital computers. The method provides an engineer who needs a quick hand solution to a set, for example, of eight equations in eight unknowns, with a simple procedure which involves only elementary algebra and no complicated rules. There are other methods requiring about the same total amount of work
^{3 ‾₆ and some which break up, as does this method, a large set of equations into several smaller sets,7,8 but it is felt that the procedure herein presented is more easily learned and more readily applied by a practical engineer. The method is also presented in matrix form in the Appendix.}