# Gauss Elimination method for solving n-linear equations in C language

This is a simple C language program that calculates solution of n-linear equations using Non-pivotal Gauss Elimination method. It uses upper triangular matrix to do so, for solution using lower triangular matrix visit here.

```#include<stdio.h>
#include<conio.h>

float matrix[10][10], m, temp[10];
int i, j, k, n;

void upper_triangularization() {
for (i=0; i<n-1; i++)
for (j=i+1; j<n; j++) {
m	= matrix[j][i]/matrix[i][i];
for (k=0; k<n+1; k++) {
matrix[j][k]	= matrix[j][k]-(m*matrix[i][k]);
}
}
} //upper_traingulisation

void back_subsitution() {
for (i=n-1; i>=0; i--) {
m	= matrix[i][n];
for (j=n-1; j>i; j--)
m	= m - temp[n-j] * matrix[i][j];
temp[n-i]	= m/matrix[i][i];
printf("\n x%d => %f", i+1, temp[n-i]);
}
} // back_subsitution

void main() {
printf("Enter number. of variables :: ");
scanf("%d", &n);

printf("Enter the augmented matrix: \n");
for (i=0; i<n; i++)
for (j=0; j<n+1; j++)
scanf("%f", &matrix[i][j]);

upper_triangularization();

printf("The upper traingular matrix is : \n");

for (i=0; i<n; i++) {
for (j=0; j<n+1; j++)
printf("%f \t", matrix[i][j]);
printf("\n");
}

printf("The required result is : \n");

back_subsitution();

getch();
} // main```