#algebra 

**Gauss-Jordan elimination** (метод Гаусса-Жордана) is a way of solving [[Systems of equations|systems of linear equations]] using the [[Matrix|reduced row-echelon form]]:

1. Put the system into row-echelon form
2. Put it into reduced row-echelon form

>[!Example]-
>![[Pasted image 20240918220110.png]]

## Leading variables
A leading variable in a linear system is one that corresponds to a leading entry in the row-echelon.
![[Pasted image 20240918220343.png]]