// Contributed by - Anuj Das ( GC University, Silchar - @ Department of Computer Science )

/* 8. Write a C program to solve the following set of equations by Gauss Elimination Method:

2.x1 + 4.x2 + 2.x3 = 15

2.x1 + x2 + 2.x3 = -54

x1 + x2 - 2.x3 = 0

*/

#include <stdio.h>

#include <stdlib.h>

void main() {

int n = 3, i, j, k; // Number of unknowns

double A[n][n+1]; // Augmented Matrix

double x[n]; // Solution

printf("Enter the Augmented Matrix:\n");

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

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

scanf("%lf", &A[i][j]);

}

}

// Gaussian Elimination

for (k = 0; k < n - 1; k++) {

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

double factor = A[i][k] / A[k][k];

for (j = k; j <= n; j++) {

A[i][j] -= factor * A[k][j];

}

}

}

// Back Substitution

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

for (i = n - 2; i >= 0; i--) {

double sum = 0.0;

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

sum += A[i][j] * x[j];

}

x[i] = (A[i][n] - sum) / A[i][i];

}

// Print Solution

printf("\nThe Solution is:\n");

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

printf("x%d: %lf\n", i + 1, x[i]);

}

}