HP 40G manual Reduced-Row Echelon Form

Reduced-Row Echelon Form

The following set of equations x – 2y +3 z		=	14
2x + y –	z	=	–	3
4x – 2y +2 z			= 14
can be written as the augmented matrix	1	– 2		3	14
	2	1		– 1	–3
	4	– 2		2	14
which can then stored as a
3 ⋅ 4 real matrix in M1.

You can use the RREF function to change this to reduced row echelon form, storing it as M2 for convenience.

The reduced row echelon matrix gives the solution to the linear equation in the forth column.

An advantage of using the RREF function is that it will also work with inconsistent matrices resulting from systems of equations which have no solution or infinite solutions.

For example, the following set of equations has an infinite number of solutions:

x + y – z = 5 2x – y = 7

x – 2y + z = 2

The final row of zeros in the reduced–row echelon form of the augmented matrix indicates an inconsistency.

12-14 Matrices