A computational procedure for reducing a set of (m × m) linear equations Axv = bv to the form MAxv = Mb,v where MAv = Uv is an upper triangular matrix. The variables of the solution vector are found by solving the resulting triangular system for one variable in the last equation, and back-substituting in the next to last equation, and so on. Some form of elimination is central to the simplex method for solving linear-programming problems. Matrices and matrix algebra; Simplex method.