Property | Value |
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Hex Value | $BB2D |
Categories | |
Localizations |
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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.
Related Commands
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 |