Property | Value |
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Hex Value | $BB2E |
Categories | |
Localizations |
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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.
Related Commands
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 |