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* Each column containing a leading {{math|1}} has zeros in all entries above the leading {{math|1}}.
While a matrix may have several echelon forms, its reduced echelon form is unique.
Given a matrix in reduced row echelon form, if one permutes the columns in order to have the leading {{math|1}} of the {{mvar|i}}th row in the {{mvar|i}}th column, one gets a matrix of the form
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