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We found one dictionary that defines the word row-reduced:

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  1. row-reduced: Wiktionary

Definitions from Wiktionary (row-reduced)

adjective:  (linear algebra) Said of a matrix which has undergone row reduction; i.e., of a matrix which has a 1 as the leading entry of each one of its non-zero rows and which has zeroes as all the other entries of any column containing such a leading entry (of any non-zero row).

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