Question

design a program that solves matrices by the gauss-jordan method use the object-oriented language c ++

Answer 1

// C++ program that solves matrices by the gauss-jordan method
// Elimination_Method
#include <bits/stdc++.h>
using namespace std;

#define M 10

// Function to print_the_matrix
void PrintMatrix(float a[][M], int n)
{
   for (int i = 0; i < n; i++) {
       for (int j = 0; j <= n; j++)
       cout << a[i][j] << " ";
       cout << endl;
   }
}

// function to reduce_matrix to reduced
// row_echelon form.
int PerformOperation(float a[][M], 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++)
               swap(a[j][k], a[j+c][k]);
       }

       for (j = 0; j < n; j++) {
          
           // Excluding all i == j
           if (i != j) {
              
               // Converting Matrix to reduced row
               // echelon form(diagonal matrix)
               float pro = a[j][i] / a[i][i];

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

// Function to print the desired_result
// if unique_solutions exists, otherwise
// prints no_solution or infinite_solutions
// depending upon the input_given.
void PrintResult(float a[][M], int n, int flag)
{
   cout << "Result is : ";

   if (flag == 2)     
   cout << "Infinite Solutions Exists" << endl;     
   else if (flag == 3)     
   cout << "No Solution Exists" << endl;
  
  
   //solution by dividing constants by
   // their respective_diagonal_elements
   else {
       for (int i = 0; i < n; i++)         
           cout << a[i][n] / a[i][i] << " ";         
   }
}

// To check whether infinite_solutions
// exists or no_solution exists
int CheckConsistency(float a[][M], 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
int main()
{
   float a[M][M] = {{ 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
   cout << "Final Augumented_Matrix is : " << endl;
   PrintMatrix(a, n);
   cout << endl;
  
   // Printing Solutions(if exist)
   PrintResult(a, n, flag);

   return 0;
}