http://learn.cemetech.net/index.php?title=TI-BASIC:Rref&feed=atom&action=historyTI-BASIC:Rref - Revision history2024-03-29T14:02:48ZRevision history for this page on the wikiMediaWiki 1.34.0http://learn.cemetech.net/index.php?title=TI-BASIC:Rref&diff=1505&oldid=prevMaintenance script: Automated internal link correction2016-02-24T23:20:49Z<p>Automated internal link correction</p>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* If the system has infinitely many solutions, it will end with rows that are all 0, including the last entry.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* If the system has infinitely many solutions, it will end with rows that are all 0, including the last entry.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>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:<del class="diffchange diffchange-inline">Matr►list(</del>|Matr►list(]] command can be used to store this column to a list.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>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:<ins class="diffchange diffchange-inline">Matr_List</ins>|Matr►list(]] command can be used to store this column to a list.</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>= Error Conditions =</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>= Error Conditions =</div></td></tr>
</table>Maintenance scripthttp://learn.cemetech.net/index.php?title=TI-BASIC:Rref&diff=575&oldid=prevMaintenance script: Initial automated import2016-02-24T18:08:07Z<p>Initial automated import</p>
<p><b>New page</b></p><div>{{Template:TI-BASIC:Command<br />
|picture=RREF.GIF<br />
|summary=Puts a matrix into reduced row-echelon form.<br />
|syntax=rref(''matrix'')<br />
|location=Press:<br />
# MATRX (on the TI-83) or 2nd MATRX (TI-83+ or higher) to access the matrix menu.<br />
# RIGHT to access the math menu.<br />
# ALPHA B to select rref(, or use arrows and ENTER.<br />
|compatibility=TI-83/84/+/SE<br />
|size=2 bytes<br />
}}<br />
<br />
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.<br />
<br />
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.<br />
<br />
[[1,2,5,0][2,2,1,2][3,4,6,2]]<br />
[[1 2 5 0]<br />
[2 2 1 2]<br />
[3 4 7 3]]<br />
rref(Ans)<br />
[[1 0 0 6 ]<br />
[0 1 0 -5.5]<br />
[0 0 1 1 ]]<br />
<br />
= Advanced Uses =<br />
<br />
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.<br />
<br />
Then, use rref( on the matrix. There are three possibilities now:<br />
* 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.<br />
* If the system is inconsistent, and has no solution, then it will end with rows that are all 0 except for the last entry.<br />
* If the system has infinitely many solutions, it will end with rows that are all 0, including the last entry.<br />
<br />
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.<br />
<br />
= Error Conditions =<br />
<br />
* '''[[TI-BASIC:Errors#invaliddim|ERR:INVALID DIM]]''' is thrown if the matrix has more rows than columns.<br />
<br />
= Related Commands =<br />
<br />
* [[TI-BASIC:Ref|Ref(]]<br />
* |- and other row operations.[[Category:TI-BASIC]]<br />
[[Category:TIBD]]</div>Maintenance script