Gauss-Jordan Elimination The code below for Gauss-Jordan Eliminaiton. Explain USING comments how the code works and how you solve a system of linear equations using this code. The system shall have three equations and three unknowns.

package com.company; // Java Implementation for Gauss-Jordan // Elimination Method class Main {

static int M = 10;

// Function to print the matrix static void PrintMatrix(float a[][], int n) { for (int i = 0; i < n; i++) { for (int j = 0; j <= n; j++) System.out.print(a[i][j] + " "); System.out.println(); } }

// function to reduce matrix to reduced // row echelon form. static int PerformOperation(float a[][], int n) { int i, j, k = 0, c, flag = 0, m = 0; float pro = 0;

// Performing elementary operations for (i = 0; i < n; i++) { if (a[i][i] == 0) { c = 1; while ((i + c) < n && a[i + c][i] == 0) c++; if ((i + c) == n) { flag = 1; break; } for (j = i, k = 0; k <= n; k++) { float temp =a[j][k]; a[j][k] = a[j+c][k]; a[j+c][k] = temp; } }

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

// Excluding all i == j if (i != j) {

// Converting Matrix to reduced row // echelon form(diagonal matrix) float p = a[j][i] / a[i][i];

for (k = 0; k <= n; k++) a[j][k] = a[j][k] - (a[i][k]) * p; } } } return flag; }

// Function to print the desired result // if unique solutions exists, otherwise // prints no solution or infinite solutions // depending upon the input given. static void PrintResult(float a[][], int n, int flag) { System.out.print("Result is : ");

if (flag == 2) System.out.println("Infinite Solutions Exists"); else if (flag == 3) System.out.println("No Solution Exists");

// Printing the solution by dividing constants by // their respective diagonal elements else { for (int i = 0; i < n; i++) System.out.print(a[i][n] / a[i][i] +" "); } }

// To check whether infinite solutions // exists or no solution exists static int CheckConsistency(float a[][], int n, int flag) { int i, j; float sum;

// flag == 2 for infinite solution // flag == 3 for No solution flag = 3; for (i = 0; i < n; i++) { sum = 0; for (j = 0; j < n; j++) sum = sum + a[i][j]; if (sum == a[i][j]) flag = 2; } return flag; }

// Driver code public static void main(String[] args) { float a[][] = {{ 0, 2, 1, 4 }, { 1, 1, 2, 6 }, { 2, 1, 1, 7 }};

// Order of Matrix(n) int n = 3, flag = 0;

// Performing Matrix transformation flag = PerformOperation(a, n);

if (flag == 1) flag = CheckConsistency(a, n, flag);

// Printing Final Matrix System.out.println("Final Augumented Matrix is : "); PrintMatrix(a, n); System.out.println("");

// Printing Solutions(if exist) PrintResult(a, n, flag); } }