What is the name of a row echelon form in which each leading entry is 1 and is the only non-zero entry in its column?

Reduced Row Echelon Form

Reduced Row Echelon Form (RREF) is the final destination of the Gauss-Jordan elimination process, used to solve systems of linear equations. By ensuring every leading entry is a 1 and the only non-zero value in its column, the solution to each variable becomes immediately apparent. A matrix in RREF is unique for any given system, making it the mathematical equivalent of a 'simplified fraction' for linear algebra.