注：

是n*n的等距矩陣，程式碼如下：

#include<iostream>
#include<math.h>
#include<fstream>
#include<stdlib.h>
using namespace std;

void print(double (*pArray)[4], int iWidth,int iHigh);

void main(){
	int n,m;
	double a[3][4] = {
		{100, 10, 1, 10},
		{400, 20, 1, 20},
		{900, 30, 1, 10},
	};//第四列是增廣矩陣

	int i,j;
	n = 3;
	cout<<"輸入方程組介數：";
	cout<<n<<endl;
	cout<<"輸入增廣矩陣："<<endl;
	for(i = 0; i < n; i++){
		for(j = 0; j < n + 1;j++){
			cout<<a[i][j]<<"   ";
		}
		cout<<endl;
	}


	for(j = 0; j < n; j++){
		double max = 0;
		double imax = 0;
		for(i = j; i < n; i++){
			if(imax < fabs(a[i][j])){
				imax = fabs(a[i][j]);
				max = a[i][j];//得到各行中所在列最大元素
				m = i;
			}
		}

		if(fabs(a[j][j]) != max) {			
			double b = 0;
			for(int k = j;k < n + 1; k++){
				b = a[j][k];
				a[j][k] = a[m][k];
				a[m][k] = b;
			}
		}

		print(a, 3, 4);

		for(int r = j;r < n + 1;r++){
			a[j][r] = a[j][r] / max;//讓該行的所在列除以所在列的第一個元素，目的是讓首元素為1
		}
		print(a, 3, 4);

		for(i = j + 1;i < n; i++){
			double c = a[i][j];
			if(c == 0)  continue;
			for(int s = j;s < n + 1;s++){
				double tempdata = a[i][s];
				a[i][s] = a[i][s] - a[j][s] * c;//前後行數相減，使下一行或者上一行的首元素為0
				print(a, 3, 4);
			}
			print(a, 3, 4);
		}
		print(a, 3, 4);
	}

	for(i = n - 2; i >= 0; i--){
		for(j = i + 1;j < n; j++){
			double tempData = a[i][j];
			double data1 = a[i][n];
			double data2 = a[j][n];
			a[i][n] = a[i][n] - a[j][n] * a[i][j];
			print(a, 3, 4);
		}
	}
	print(a, 3, 4);
	
	cout<<"方程組的解是："<<endl;
	for(int k = 0; k < n; k++){
		cout<<"x"<<k<<" = "<<a[k][n]<<endl;
	}
}


void print(double (*pArray)[4], int iWidth,int iHigh) {
	std::cout<<"Array: "<<"\n";
	for(int i = 0; i < iWidth; i++){
		for(int j = 0; j < iHigh;j++){
			cout<<pArray[i][j]<<"   ";
		}
		cout<<endl;
	}
}