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I'm currently studying methods to solve systems of linear equations. With the Gauss Jordan elimination, I was wondering if there were any requirements or conditions required for the method to work with a system.

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  • $\begingroup$ Depends on what you mean by "work". And what sort of generality do you want to work in? $\endgroup$ Commented Dec 11, 2017 at 13:32

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No, one of the beauty of Gauss-Jordan elimination is that you can always apply it, as long as you work over the real $\mathbb{R}$ or complex numbers $\mathbb{C}.$

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The general requirement is that we work over a field, i.e. all non-zero elements have an inverse.
Once you have that, the Gauss Jordan elimination will work for any matrix; assuming, of course, that you can actually do computations in said field.

There are variants of the algorithm for different rings, but I am not aware of a general version that works for all rings; it's more like "in this special ring, we have property X, which helps us to do the algorithm as follows...".

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