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## Gauss-Jordan reduction: rref gaussjord

rref solves a linear system of equations written in matrix form (see also 1.31.17) :
A*X=B
rref takes one or two arguments.
• If rref has only one argument, this argument is the augmented matrix of the system (the matrix obtained by augmenting matrix A to the right with the column vector B).
The result is a matrix [A1,B1] : A1 has zeros both above and under its principal diagonal and has 1 on its principal diagonal, and the solutions of:
A1*X=B1
are the same as :
A*X=B
For example, to solve the system:

input :
rref([[3,1,-2],[3,2,2]])
Output :
[[1,0,-2],[0,1,4]]
Hence x = - 2 and y = 4 is the solution of this system.

rref can also solve several linear systems of equations having the same first member. We write the second members as a column matrix.
Input :

rref([[3,1,-2,1],[3,2,2,2]])
Output :
[[1,0,-2,0],[0,1,4,1]]
Which means that (x = - 2 and y = 4) is the solution of the system

and (x = 0 and y = 1) is the solution of the system

• If rref has two parameters, the second parameter must be an integer k, and the Gauss-Jordan reduction will be performed on (at most) the first k columns.
Input :
rref([[3,1,-2,1],[3,2,2,2]],1)
Output :
[[3,1,-2,1],[0,1,4,1]]

suivant: Solving A*X=B : simult monter: Linear systems précédent: Gauss reduction of a   Table des matières   Index
giac documentation written by Renée De Graeve and Bernard Parisse