Property	Value
Hex Value	`$BB2E`
Categories	Catalog > R Matrix > Math
Localizations	FR: `Gauss-Jordan(`

`rref(`

Overview

Returns the reduced row-echelon form of a matrix.

Availability: Token available everywhere.

Syntax

rref(matrix)

Arguments

Name	Type	Optional
matrix	matrix

Location

2nd, matrix, MATH, B:rref(

Description

Given a matrix with at least as many columns as rows, the rref( command puts a matrix into reduced row-echelon form using Gaussian elimination.

This means that as many columns of the result as possible will contain a pivot entry of 1, with all entries in the same column, or to the left of the pivot, being 0.

[[1,2,5,0][2,2,1,2][3,4,6,2]]
    [[1 2 5 0]
     [2 2 1 2]
     [3 4 7 3]]
rref(Ans)
    [[1 0 0 6   ]
     [0 1 0 -5.5]
     [0 0 1 1   ]]

Advanced Uses

The rref( command can be used to solve a system of linear equations. First, take each equation, in the standard form of $a_1x_1+\dots + a_nx_n = b$, and put the coefficients into a row of the matrix.

Then, use rref( on the matrix. There are three possibilities now:

If the system is solvable, the left part of the result will look like the identity matrix. Then, the final column of the matrix will contain the values of the variables.
If the system is inconsistent, and has no solution, then it will end with rows that are all 0 except for the last entry.
If the system has infinitely many solutions, it will end with rows that are all 0, including the last entry.

This process can be done by a program fairly easily. However, unless you're certain that the system will always have a unique solution, you should check that the result is in the correct form, before taking the values in the last column as your solution. The Matr►list( command can be used to store this column to a list.

Error Conditions

ERR:INVALID DIM is thrown if the matrix has more rows than columns.

Source: parts of this page were written by the following TI|BD contributors: Battlesquid, DarkerLine, GoVegan, kg583.

History

Calculator	OS Version	Description
TI-83	0.01013	Added

Authors: Adrien Bertrand

rref(