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Row Echelon Form
Definition: A matrix is in row echelon form if it satisfies the following properties: 1) Any rows consisting entirely of zeros are at the bottom. 2) In each nonzero row, the first nonzero entry (called the leading entry) is in a column to the left of any leading entries below it.
Source: Linear Algebra: A Modern Introduction, 3rd edition by David Poole (note-custom edition titled Matrix Algebra)