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))
