Python sympy | Matrix.rref () method

Michael Zippo

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) )