Gauss_Elimination

#include <stdio.h>
int main()
{
    int n;
    printf("Enter the number of variables: ");
    scanf("%d", &n);
    float A[n][n + 1];
    float x[n + 1];

    printf("Enter the elements of augmented matrix row-wise:\n");
    for (int i = 1; i <= n; i++)
    {
        for (int j = 1; j <= (n + 1); j++)
        {
            scanf("%f", &A[i][j]);
        }
    }
    printf("\n");

    int temp = 0;
    if (A[1][1] == 0 && A[2][1] != 0)
    {
        for (int j = 1; j <= n + 1; j++)
        {
            temp = A[1][j];
            A[1][j] = A[2][j];
            A[2][j] = temp;
        }
    }
    else if (A[1][1] == 0 && A[3][1] != 0)
    {
        for (int j = 1; j <= n + 1; j++)
        {
            temp = A[1][j];
            A[1][j] = A[3][j];
            A[3][j] = temp;
        }
    }
    else if (A[1][1] == 0 && A[2][1] == 0 && A[3][1] == 0)
    {
        printf("Invalid Input\n");
    }

    printf("Augmented Matrix: \n");
    for (int i = 1; i <= n; i++)
    {
        for (int j = 1; j <= n + 1; j++)
        {
            printf("%f ", A[i][j]);
        }
        printf("\n");
    }

    for (int j = 1; j <= n; j++) /* loop for the generation of upper triangular matrix*/
    {
        for (int i = 1; i <= n; i++)
        {
            if (i > j)
            {
                float c = A[i][j] / A[j][j];
                for (int k = 1; k <= n + 1; k++)
                {
                    A[i][k] = A[i][k] - c * A[j][k];
                }
            }
        }
    }

    printf("\nUpper Triangular Matrix: \n");
    for (int i = 1; i <= n; i++)
    {
        for (int j = 1; j <= n + 1; j++)
        {
            printf("%f ", A[i][j]);
        }
        printf("\n");
    }

    x[n] = A[n][n + 1] / A[n][n];

    /* this loop is for backward substitution*/
    for (int i = n - 1; i >= 1; i--)
    {
        float sum = 0.0;
        for (int j = i + 1; j <= n; j++)
        {
            sum = sum + A[i][j] * x[j];
        }
        x[i] = (A[i][n + 1] - sum) / A[i][i];
    }

    printf("\nThe solution is:");
    for (int i = 1; i <= n; i++)
    {
        printf("\n%d %f", i + 1, x[i]);
    }
    printf("\n");

    return 0;
}