How to calculate the reduced row echelon form of a matrix using Python?

We can use the sympy Python library to calculate the row echelon form of a matrix. We can use the following Python code for that purpose:

import sympy
import numpy

n = 3
A = numpy.random.randint(low=1, high=10, size=(n, n))
B = sympy.Matrix(A).rref()

print("Matrix A: \n", A)
print("The Row Echelon Form of A: \n", B)

Here, we are first creating a matrix with random integers. We are using the numpy.random.randint() function to generate random integers for that purpose. The generated integers will be within the range [low, high). And the size=(n, n) indicates that the created matrix will have n rows and n columns.

Now, we use the sympy.Matrix(A) function to create a sympy matrix from A. And then, we use the rref() function to calculate the reduced row echelon form of the matrix.

The output of the mentioned program will be:

Matrix A: 
 [[7 8 5]
 [2 4 3]
 [2 5 7]]
The Row Echelon Form of A: 
 (Matrix([
[1, 0, 0],
[0, 1, 0],
[0, 0, 1]]), (0, 1, 2))

Please note that the rref() function returns the reduced row echelon form of the matrix A and a tuple that indicates the indices of the pivot columns. In our case, the column indices of the pivots are 0, 1, and 2. So, the rref() function returns (0, 1, 2) as the second returned element. The first returned element is the reduced row echelon form of the matrix A.