Maintenance script: Automated internal link correction

2016-02-24T23:20:49Z

Automated internal link correction

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	* If the system has infinitely many solutions, it will end with rows that are all 0, including 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 [[TI-BASIC:~~Matr►list(~~\|Matr►list(]] command can be used to store this column to a list.		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 [[TI-BASIC:Matr_List\|Matr►list(]] command can be used to store this column to a list.

	= Error Conditions =		= Error Conditions =

Maintenance script: Initial automated import

2016-02-24T18:08:07Z

Initial automated import

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{{Template:TI-BASIC:Command
|picture=RREF.GIF
|summary=Puts a matrix into reduced row-echelon form.
|syntax=rref(''matrix'')
|location=Press:
# MATRX (on the TI-83) or 2nd MATRX (TI-83+ or higher) to access the matrix menu.
# RIGHT to access the math menu.
# ALPHA B to select rref(, or use arrows and ENTER.
|compatibility=TI-83/84/+/SE
|size=2 bytes
}}

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 <math>\definecolor{darkgreen}{rgb}{0.90,0.91,0.859}\pagecolor{darkgreen}a_1x_1+\dots + a_nx_n = b</math>, 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 [[TI-BASIC:Matr►list(|Matr►list(]] command can be used to store this column to a list.

= Error Conditions =

* '''[[TI-BASIC:Errors#invaliddim|ERR:INVALID DIM]]''' is thrown if the matrix has more rows than columns.

= Related Commands =

* [[TI-BASIC:Ref|Ref(]]
* |- and other row operations.[[Category:TI-BASIC]]
[[Category:TIBD]]

TI-BASIC:Rref - Revision history

Maintenance script: Automated internal link correction

Maintenance script: Initial automated import