Property	Value
Hex Value	`$BB2D`
Categories	Catalog > R Matrix > Math
Localizations	FR: `Gauss(`

`ref(`

Overview

Returns the row-echelon form of a matrix.

Availability: Token available everywhere.

Syntax

ref(matrix)

Arguments

Name	Type	Optional
matrix	matrix

Location

2nd, matrix, MATH, A:ref(

Description

Given a matrix with at least as many columns as it has rows, the ref( command uses a technique called Gaussian elimination to put the matrix into row-echelon form.

This means that the leftmost N columns (if the matrix has N rows) of the matrix are upper triangular - all entries below the main diagonal are zero. What's more, every entry on the main diagonal is either 0 or 1.

[[1,2,5,0][2,2,1,2][3,4,6,2]]
    [[1 2 5 0]
     [2 2 1 2]
     [3 4 6 2]
ref(Ans)►Frac
    [[1 4/3 2   2/3]
     [0 1   9/2 -1 ]
     [0 0   0   0  ]]

Advanced Uses

In theory, a system of linear equations in N variables can be solved using the ref( command - an equation of the form $a_1x_1+\dots + a_nx_n = b$ becomes a row $a_1, \dots, a_n, b$, and is put into the matrix. If there is a sufficient number of conditions, the last row of the reduced matrix will give you the value of the last variable, and back-substitution will give you the others.

In practice, it's easier to use rref( instead for the same purpose.

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: DarkerLine, GoVegan, kg583, Timothy Foster.

History

Calculator	OS Version	Description
TI-83	0.01013	Added

Authors: Adrien Bertrand

ref(