The following code implements Gaussian Elimination to solve Ax=b. What is the error?

import numpy as np

def gaussian_elimination(A, b):

    n = len(b)

    A = A.astype(float)

    b = b.astype(float)

    for k in range(n):

        # Partial pivoting

        max_row = np.argmax(np.abs(A[k:, k])) + k

        A[[k, max_row]] = A[[max_row, k]]

        b[[k, max_row]] = b[[max_row, k]]

        # Elimination

        for i in range(k+1, n):

            factor = A[i, k] / A[k, k]

            A[i, k:] -= factor * A[k, k:]

            b[i] -= factor * b[k]

    # Back substitution

    x = np.zeros(n)

    for k in range(n-1, -1, -1):

        x[k] = (b[k] - np.dot(A[k, k+1:], x[k+1:])) / A[k, k]

    return x

# Test case

A = np.array([[2, 1, -1], [4, 1, 0], [1, -1, 1]])

b = np.array([1, -2, 3])

print(gaussian_elimination(A, b))