Gaussian Elimination

A sequence of elementary row (and optionally column) operations applied to a matrix to transform it into row-echelon or reduced row-echelon form, used to solve linear systems, compute rank, find inverses, and obtain bases for solution spaces by systematic elimination of variables.

A systematic procedure of applying elementary row operations (and, when needed, column permutations) to a matrix to produce an echelon or reduced echelon form; used to solve linear systems, compute rank, and derive inverses or factorizations such as LU (with pivoting and permutations as required).