PYTHON CODE MODIFICATION TO NOT INCLUDE NUMPY (OR ANY OTHER IMPORTED LIBRARIES OR MODULES)

Hi, how can I modify this code so that it produces the same output but doesn't require the use of an imported library such as NumPy? This code is used for Gaussian Elimination given matrix A and vector b. I want to learn how I can code without needing these pre-built functions. Thanks!

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import numpy as np

# Define the matrix A and vector b A = np.array([[1, 0, 2], [2, -1, 3], [4, 1, 8]], dtype=float) b = np.array([1, -1, 2], dtype=float)

# Combine matrix A and vector b into augmented matrix C C = np.column_stack((A, b))

# Set E to 1 (check to see if a unique solution exists) E = 1

# Get the size of the matrix n = C.shape[0]

# Iterate over each column j for j in range(n): # Find the index of the row with the maximum absolute value in column j p = np.argmax(np.abs(C[j:, j])) + j # If the maximum value is 0, set E to 0 and exit if C[p, j] == 0: E = 0 break # If the pivot is not in the j-th row, swap the rows if p != j: C[[j, p], :] = C[[p, j], :] # Eliminate the entries below the pivot in column j for i in range(j+1, n): C[i, :] -= (C[i, j]/C[j, j]) * C[j, :]

# Check if a unique solution was found if E == 1: # Initialize the solution vector x with zeros x = np.zeros(n)

# Back-substitution to solve for x for j in range(n-1, -1, -1): x[j] = (C[j, -1] - np.dot(C[j, j+1:n], x[j+1:n])) / C[j, j]

# Print the solution print("The solution is: ", x) else: print("The algorithm failed to find a unique solution.")

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Please provide a screenshot of the working code. Thank you. Will upvote.