row echelon form
A matrix shape where each row's leading entry steps right of the one above — the target of Gaussian elimination.
A matrix is in row echelon form (REF) when each row's leading nonzero entry sits strictly to the right of the leading entry in the row above it, with any all-zero rows pushed to the bottom. It is in reduced row echelon form (RREF) when, further, every leading entry equals 1 and is the only nonzero entry in its column — at that point the solution can be read directly off the matrix.
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