3.7.1 Reduce

This transformation applies Gauss-Jordan elimination to a matrix to transform it to reduced row echelon form.

As used in linear algebra, the coefficients and constant terms of a system of equations can be represented by a matrix. Transforming the matrix to reduced row-echelon form is a step toward obtaining a solution to the system of equations.

For example, given the set of equations x+2⋅y+3⋅z=0, 3⋅x+4⋅y+7⋅z=2 and 6⋅x+5⋅y+9⋅z=11, the matrix expression of coefficients [(1, 2, 3), (3, 4, 7), (6, 5, 9)]‖[(, 0), (, 2), (, 11)] can be simplified to [(1, 2, 3, 0), (3, 4, 7, 2), (6, 5, 9, 11)]. Applying Reduce results in [(1, 0, 0, 4), (0, 1, 0, 1), (0, 0, 1, -2)], providing a final result of x=4, y=1 and z=-2.

Contrast this with the techniques in §3.5.1.2, §3.6.6 and §3.7.2.

Reduction is performed symbolically. For a matrix of variables, like