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I work as a tutor for linear algebra. Students will often have a problem that requires them to row reduce, and they'll make an arithmetic mistake somewhere. Often they'll ask for my help finding their mistake.

I often will go through the operations myself, but it takes a bit of time. Do you have any recommendations for an online app that can check each row operation? Ideally the app would:

  • Display previous matrices, and the row operations that led to each.
  • Allow you to "go back" if you made a mistake.

I've found a couple ones, like this one: https://www.zweigmedia.com/RealWorld/tutorialsf1/scriptpivotold.html. However, it doesn't print the previous versions of the matrix, and it doesn't let you "go back."

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  • $\begingroup$ Wolfram Alpha can do this. Not sure this is an appropriate question for this site. You might want to consider searching for a similar question asked on Mathematics, and if you can't find it in a search, ask it as a new question. This is a question any student might be interested in, as well, so hardly specific to math educators. $\endgroup$ – Namaste Sep 12 at 18:32
  • $\begingroup$ Wolfram Alpha example of row reduction in a $2\times 3$ matrix. $\endgroup$ – Namaste Sep 12 at 18:50
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    $\begingroup$ I think this is a valid question for this site, since educators definitely might ask this (checking this stuff by hand in HW/exams is torture, I've certainly done it enough), but you may want to consider how to make your question more useful specifically for the educational context. Hope you find one! $\endgroup$ – kcrisman Sep 12 at 19:48
  • $\begingroup$ One possible solution is to use Sagemath, cfm.brown.edu/people/dobrush/am34/sage/echelon.html $\endgroup$ – Jaakko Seppälä Sep 13 at 8:35
  • $\begingroup$ @XanderHenderson: Changed. $\endgroup$ – user12682 Sep 17 at 18:15
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This is a nice facility. It requires Adobe/Flash. It is by Dan Gries.

You can set the matrix size and enter your data. Then the site provides you with three operations: swap two rows, add a multiple of a row to another, or multiply a row by a number. Just the basic elementary row operations. Student is expected to know the Gauss or Gauss-Jordan operation. So that one can perform the process while the app does the arithmetic. A life saver for linear algebra student, without giving away the final answer!

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  • $\begingroup$ That's almost exactly what I was looking for. Thank you so much! $\endgroup$ – user12682 Sep 12 at 20:33
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    $\begingroup$ Except Flash is EOL at the end of 2020, right? Does anyone know if the site would be updated with HTML5 or other interactive capabilities? $\endgroup$ – kcrisman Sep 13 at 18:02

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