Gauss-Jordan reduction:

- 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``A*X=B``rref([[3,1,-2],[3,2,2]])``[[1,0,-2],[0,1,4]]`*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]])``[[1,0,-2,0],[0,1,4,1]]`*x*= - 2 and*y*= 4) is the solution of the system*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)``[[3,1,-2,1],[0,1,4,1]]`