SolveLinearEquation

import numpy as np

def gauss_elimination(a, b):
    n = len(b)
    isSolutionExists = True
    errorMessage = "The system has no roots of equations or has an infinite set of them."

    # Forward Elimination
    for i in range(n):
        # Find pivot
        max_row = i
        for j in range(i+1, n):
            if abs(a[j][i]) > abs(a[max_row][i]):
                max_row = j
        # Swap rows
        a[i], a[max_row] = a[max_row], a[i]
        b[i], b[max_row] = b[max_row], b[i]

        # Check if matrix is singular
        if abs(a[i][i]) < 1e-12:
            isSolutionExists = False
            return (isSolutionExists, errorMessage)

        # Eliminate column
        for j in range(i+1, n):
            ratio = a[j][i]/a[i][i]
            for k in range(i, n):
                a[j][k] -= ratio * a[i][k]
            b[j] -= ratio * b[i]

    # Backward Substitution
    x = [0 for i in range(n)]
    for i in range(n-1, -1, -1):
        x[i] = b[i]
        for j in range(i+1, n):
            x[i] -= a[i][j] * x[j]
        x[i] /= a[i][i]

    # Calculate residual errors
    r = np.dot(a, x) - b

    return (isSolutionExists, x, r)

# Example usage:
n = 3
a = [[3.0, 2.0, -4.0], [2.0, 3.0, 3.0], [5.0, -3.0, 1.0]]
b = [3.0, 15.0, 14.0]

result = gauss_elimination(a,b)

if result[0]:
    print("x:")
    for i in range(n):
        print(result[1][i])
    print("r:")
    for i in range(n):
        print(result[2][i])
else:
    print(result[1])