# Python sympy | Matrix.rref () method

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Using the sympy.Matrix () method. Rref () we can put the matrix in a reduced row row ... Matrix (). Rref () returns a tuple of two elements. The first — this is a reduced row row, and the second — tuple of pivot column indices.

Syntax: Matrix (). rref ()

Returns: Returns a tuple of which first element is of type Matrix and second one is of type tuple.

Example # 1:

 ` # import sympy ` ` from ` ` sympy ` ` import ` ` * ` ` M ` ` = ` ` Matrix ([ [` ` 1 ` `, ` ` 0 ` `, ` ` 1 ` `, ` ` 3 ` `], [` ` 2 ` `, ` ` 3 ` `, ` ` 4 ` `, ` ` 7 ` `], [` ` - ` ` 1 ` `, ` ` - ` ` 3 ` `, ` ` - ` ` 3 ` `, ` ` - ` ` 4 ` `]]) ` ` print ` ` (` ` "Matrix: {}" ` `. ` ` format ` ` (M)) ` ` # Use the sympy.rref () method ` ` M_rref ` ` = ` ` M.rref () ` ` ` ` print ` ` (` `" The Row echelon form of matrix M and the pivot columns: {} "` `. ` ` format ` ` (M_rref)) `

Output:

` Matrix: Matrix ([[1, 0, 1, 3], [2, 3, 4, 7], [-1, -3, -3, - 4]]) The Row echelon form of matrix M and the pivot columns: (Matrix ([[1, 0, 1, 3], [0, 1, 2/3, 1/3], [0, 0, 0 , 0]]), (0, 1)) `

Example # 2:

` `

` # import sympy from sympy import * M = Matrix ([[ 14 , 0 , 11 , 3 ], [ 22 , 23 , 4 , 7 ], [ - 12 , - 34 , - 3 , - 4 ]]) print ( "Matrix: {}" . format (M)) # Use the sympy.rref () method M_rref = M.rref () print ( "The Row echelon form of matrix M and the pivot columns: { } " . format (M_rref)) `

` `

Exit :

` Matrix: Matrix ([[14, 0, 11, 3], [22, 23, 4, 7], [-12, -34, -3, -4]]) The Row echelon form of matrix M and the pivot columns: (Matrix ([[1, 0, 0, 1405/4254], [0, 1, 0, 10/709], [0, 0, 1, -314/2127]]), (0, 1, 2) ) `

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