4. Write a program to demonstrate Gauss Elimination Method.

            
    /*Program to execute Gauss Elimination method */
    #include <stdio.h>
    #include <math.h>
    #include <conio.h>
    #define max 10
    void main()
    {
        int i, j, k, n;
        float t = 0, sol, a[max][max + 1], x[max];
        clrscr();
        printf("Enter number of equations\n");
        scanf("%d", &n);
        printf("Input data for arugement matrix: \n");
        for (i = 0; i < n; i++)
        {
            for (j = 0; j <= n; j++)
            {
                scanf("%f", &a[i][j]);
            }
        }
        for (j = 0; j < n - 1; j++)
        {
            for (i = j + 1; i < n; i++)
            {
                t = a[i][j] / a[j][j];
                for (k = 0;
                     k <= n;
                     k++)
                {
                    a[i][k] = a[i][k] - a[j][k] * t;
                }
            }
        }
        printf("\n The upper triangular matrix is: \n");
        for (i = 0; i < n; i++)
        {
            for (j = 0; j <= n; j++)
            {
                printf("%f\t", a[i][j]);
            }
            printf("\n");
        }
        for (i = 0; i < n; i++)
            x[i] = 0;
        for (i = n - 1; i >= 0; i--)
        {
            sol = 0;
            for (j = 0; j < n; j++)
            {
                sol = sol + a[i][j] * x[j];
            }
            x[i] = (a[i][n] - sol) / a[i][i];
        }
        printf("\n\n The solution is: ");
        for (i = 0; i < n; i++)
        {
            printf("\nElement %d: %f: ", i + 1, x[i]);
        }
        getch();
    }