##  [Gaussian Elimination](/index.php/gaussian-elimination) 

  ##  [Gaussian Elimination](https://puremath.quantumdictionary.io/gaussian-elimination-0) 

  

 [![Pure Mathematics Dictionary](/sites/default/files/styles/large/public/2026-01/Pure%20Mathematics.png.webp?itok=5pZnFQ59)](/index.php/topic-specific-dictionaries/mathematics-logic/pure-mathematics)

- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

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.

 

 

 

 

 





 

 



 ##  [Gaussian Elimination](https://algebra.quantumdictionary.io/gaussian-elimination-1) 

  

 [![Algebra](/sites/default/files/styles/large/public/2026-01/Algebra.png.webp?itok=3pHxBnUF)](/index.php/topic-specific-dictionaries/pure-mathematics/algebra)

- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

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).