## C++, , gaussian_elimination.cpp

``````/**
* \file
* \brief [Gaussian elimination
* method](https://en.wikipedia.org/wiki/Gaussian_elimination)
*/
#include <iostream>

/** Main function */
int main() {
int mat_size, i, j, step;

std::cout << "Matrix size: ";
std::cin >> mat_size;

// create a 2D matrix by dynamic memory allocation
double **mat = new double *[mat_size + 1], **x = new double *[mat_size];
for (i = 0; i <= mat_size; i++) {
mat[i] = new double[mat_size + 1];
if (i < mat_size)
x[i] = new double[mat_size + 1];
}

// get the matrix elements from user
std::cout << std::endl << "Enter value of the matrix: " << std::endl;
for (i = 0; i < mat_size; i++) {
for (j = 0; j <= mat_size; j++) {
std::cin >>
mat[i][j];  // Enter (mat_size*mat_size) value of the matrix.
}
}

// perform Gaussian elimination
for (step = 0; step < mat_size - 1; step++) {
for (i = step; i < mat_size - 1; i++) {
double a = (mat[i + 1][step] / mat[step][step]);

for (j = step; j <= mat_size; j++)
mat[i + 1][j] = mat[i + 1][j] - (a * mat[step][j]);
}
}

std::cout << std::endl
<< "Matrix using Gaussian Elimination method: " << std::endl;
for (i = 0; i < mat_size; i++) {
for (j = 0; j <= mat_size; j++) {
x[i][j] = mat[i][j];
std::cout << mat[i][j] << " ";
}
std::cout << std::endl;
}
std::cout << std::endl
<< "Value of the Gaussian Elimination method: " << std::endl;
for (i = mat_size - 1; i >= 0; i--) {
double sum = 0;
for (j = mat_size - 1; j > i; j--) {
x[i][j] = x[j][j] * x[i][j];
sum = x[i][j] + sum;
}
if (x[i][i] == 0)
x[i][i] = 0;
else
x[i][i] = (x[i][mat_size] - sum) / (x[i][i]);

std::cout << "x" << i << "= " << x[i][i] << std::endl;
}

for (i = 0; i <= mat_size; i++) {
delete[] mat[i];
if (i < mat_size)
delete[] x[i];
}
delete[] mat;
delete[] x;

return 0;
}
``````