A new method for solving simultaneous linear equations associated with multivariate analysis

A method is outlined whereby the equations resulting from multivariate analyses may be solved. Only the upper or lower triangular coefficient matrix need be employed. All solutions involving any combination(s) of the variables represented in the coefficient matrix are readily obtainable without permutation of the matrix. All solutions are given immediately without the need for back solving. One variable is added to or subtracted from the regression equation with each application of the method. The method may be applied as repeatedly as needed for any particular solution.