Python sympy | Matrix.rref() method

With the help of sympy.Matrix().rref() method, we can put a matrix into reduced Row echelon form. Matrix().rref() returns a tuple of two elements. The first is the reduced row echelon form, and the second is a tuple of indices of the pivot columns.

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 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 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([[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))