#math/linear_algebra 


A [[systems of linear equations and matrices.|system of linear equations]] can be solved via matrix reduction into [[matrix representation of systems of linear equations#solve|row echelon form or reduced row echelon form]]. 

Gaussian Elimination ::: put an augmented matrix into [[matrix representation of systems of linear equations#solve#reduced row echelon form|row echelon form]] and solve by back substitution.

Gauss-Jordan Elimination ::: Put augmented matrix in [[matrix representation of systems of linear equations#solve#reduced row echelon form|***reduced*** row echelon]] form and solve by back substitution.