Maintenance script: Initial automated import

2016-02-24T18:05:25Z

Initial automated import

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{{Template:TI-BASIC:Command
|picture=REF.GIF
|summary=Puts a matrix into row-echelon form.
|syntax=ref(''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 submenu.
# ALPHA A to select ref(, or use arrows.
|compatibility=TI-83/84/+/SE
|size=2 bytes
}}

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 <math>a_1x_1+\dots + a_nx_n = b</math> becomes a row <math>a_1, \dots, a_n, b</math>, 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 [[TI-BASIC:Rref|Rref(]] instead for the same purpose.

= Error Conditions =

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

= Related Commands =

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

TI-BASIC:Ref - Revision history

Maintenance script: Initial automated import