using System;

public class Program

{

    public static void Main()

    {

    // Santiago Gonzalez Ponce - 3088820

    // Josue Gerardo Lozano Suarez - 3081284

    int n = 7;

        double[,] matrix = new double[n, n + 1];

        Random random = new Random();

        Console.WriteLine("Matriz original (7x7 con términos independientes):");

        for (int i = 0; i < n; i++)

        {

            for (int j = 0; j <= n; j++)

            {

                matrix[i, j] = random.Next(-10, 11);

                Console.Write(matrix[i, j] + "\t");

            }

            Console.WriteLine();

        }

        double[,] originalMatrix = (double[,])matrix.Clone();

        if (GaussEliMet(matrix))

        {

            Console.WriteLine("\nMatriz final después de la eliminación de Gauss:");

            PrintMatrix(matrix);

            double[] solution = SutiRegre(matrix);

            Console.WriteLine("\nLa solución del sistema es:");

            for (int i = 0; i < n; i++)

            {Console.WriteLine($"x{i + 1} = {solution[i]}");}

        }

        else

        {Console.WriteLine("\nLa matriz no tiene solución.");}

    }

    static bool GaussEliMet(double[,] mat)

    {

        int n = 7;

        for (int i = 0; i < n; i++)

        {

            int max = i;

            for (int k = i + 1; k < n; k++)

            {

                if (Math.Abs(mat[k, i]) > Math.Abs(mat[max, i]))

                {max = k;}

            }

            for (int k = i; k < n + 1; k++)

            {

                double temp = mat[max, k];

                mat[max, k] = mat[i, k];

                mat[i, k] = temp;

            }

            if (Math.Abs(mat[i, i]) < 1e-10)

            {

                return false;

            }

            for (int k = i + 1; k < n; k++)

            {

                double factor = mat[k, i] / mat[i, i];

                for (int j = i; j < n + 1; j++)

                {

                    mat[k, j] -= factor * mat[i, j];

                }

            }

        }

        return true; 

    }

    static double[] SutiRegre(double[,] mat)

    {

        int n = 7;

        double[] result = new double[n];

        for (int i = n - 1; i >= 0; i--)

        {

            result[i] = mat[i, n];

            for (int j = i + 1; j < n; j++)

            {

                result[i] -= mat[i, j] * result[j];

            }

            result[i] /= mat[i, i];

        }

        return result;

    }

    static void PrintMatrix(double[,] mat)

    {

        int n = 7;

        for (int i = 0; i < n; i++)

        {

            for (int j = 0; j <= n; j++)

            {

                Console.Write(mat[i, j] + "\t");

            }

            Console.WriteLine();

        }

    }

}