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## Main Question or Discussion Point

I have been looking for a proof of correctness of Gaussian elimination, but alas, without much success. Most online resources explain how to apply the algorithm rather than proving correctness. That said, I have been looking for a proof to the following theorem, which is stated in Friedberg's linear algebra:

Gaussian elimination transforms a matrix into its row echelon form.

I would appreciate any help/links to a proof of this theorem. I am almost certain it involves mathematical induction on the number of rows in the matrix, but am having trouble proving it myself.

Thanks!

BiP

Gaussian elimination transforms a matrix into its row echelon form.

I would appreciate any help/links to a proof of this theorem. I am almost certain it involves mathematical induction on the number of rows in the matrix, but am having trouble proving it myself.

Thanks!

BiP