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  1. #include<iostream>
  2. #include<iomanip>
  3. using namespace std;
  4.  
  5. const int MAX = 10;
  6.  
  7. // Function to calculate determinant of a matrix
  8. double determinant(double mat[MAX][MAX], int n) {
  9.     double det = 0;
  10.     if(n == 1)
  11.         return mat[0][0];
  12.     if(n == 2)
  13.         return (mat[0][0]*mat[1][1] - mat[0][1]*mat[1][0]);
  14.  
  15.     double temp[MAX][MAX];
  16.     int sign = 1;
  17.  
  18.     for(int f=0; f<n; f++) {
  19.         int subi = 0;
  20.         for(int i=1; i<n; i++) {
  21.             int subj = 0;
  22.             for(int j=0; j<n; j++) {
  23.                 if(j == f)
  24.                     continue;
  25.                 temp[subi][subj] = mat[i][j];
  26.                 subj++;
  27.             }
  28.             subi++;
  29.         }
  30.         det += sign * mat[0][f] * determinant(temp, n-1);
  31.         sign = -sign;
  32.     }
  33.     return det;
  34. }
  35.  
  36. // Function to get cofactor matrix for adjoint
  37. void getCofactor(double mat[MAX][MAX], double temp[MAX][MAX], int p, int q, int n) {
  38.     int i = 0, j = 0;
  39.     for(int row=0; row<n; row++) {
  40.         for(int col=0; col<n; col++) {
  41.             if(row != p && col != q) {
  42.                 temp[i][j++] = mat[row][col];
  43.                 if(j == n-1) {
  44.                     j = 0;
  45.                     i++;
  46.                 }
  47.             }
  48.         }
  49.     }
  50. }
  51.  
  52. // Function to calculate adjoint
  53. void adjoint(double mat[MAX][MAX], double adj[MAX][MAX], int n) {
  54.     if(n == 1) {
  55.         adj[0][0] = 1;
  56.         return;
  57.     }
  58.  
  59.     double temp[MAX][MAX];
  60.     int sign = 1;
  61.  
  62.     for(int i=0; i<n; i++) {
  63.         for(int j=0; j<n; j++) {
  64.             getCofactor(mat, temp, i, j, n);
  65.             sign = ((i+j)%2 == 0) ? 1 : -1;
  66.             adj[j][i] = sign * determinant(temp, n-1);
  67.         }
  68.     }
  69. }
  70.  
  71. // Function to calculate inverse
  72. void inverse(double mat[MAX][MAX], double inv[MAX][MAX], int n, double det) {
  73.     double adj[MAX][MAX];
  74.     adjoint(mat, adj, n);
  75.  
  76.     for(int i=0; i<n; i++)
  77.         for(int j=0; j<n; j++)
  78.             inv[i][j] = adj[i][j] / det;
  79. }
  80.  
  81. int main() {
  82.     int n;
  83.     double A[MAX][MAX], B[MAX], X[MAX], Atemp[MAX][MAX], detA;
  84.  
  85.     cout << "Enter the order of square matrix: ";
  86.     cin >> n;
  87.  
  88.     cout << "Enter coefficients of matrix A:\n";
  89.     for(int i=0; i<n; i++)
  90.         for(int j=0; j<n; j++)
  91.             cin >> A[i][j];
  92.  
  93.     cout << "Enter constants of vector B:\n";
  94.     for(int i=0; i<n; i++)
  95.         cin >> B[i];
  96.  
  97.     // Find determinant of A
  98.     detA = determinant(A, n);
  99.     cout << fixed << setprecision(4);
  100.     cout << "\nDeterminant of A: " << detA << endl;
  101.  
  102.     if(detA == 0) {
  103.         cout << "Matrix is singular; the system is not uniquely solvable.\n";
  104.         return 0;
  105.     }
  106.  
  107.     // Solve using Cramer's Rule
  108.     for(int i=0; i<n; i++) {
  109.         // Copy A into Atemp
  110.         for(int r=0; r<n; r++)
  111.             for(int c=0; c<n; c++)
  112.                 Atemp[r][c] = A[r][c];
  113.  
  114.         // Replace i-th column with vector B
  115.         for(int r=0; r<n; r++)
  116.             Atemp[r][i] = B[r];
  117.  
  118.         double detAi = determinant(Atemp, n);
  119.         X[i] = detAi / detA;
  120.     }
  121.  
  122.     // Display solution
  123.     cout << "\nThe solution using Cramer's Rule:\n";
  124.     for(int i=0; i<n; i++)
  125.         cout << "x" << i+1 << " = " << X[i] << endl;
  126.  
  127.     // Compute and display inverse (optional)
  128.     double inv[MAX][MAX];
  129.     inverse(A, inv, n, detA);
  130.  
  131.     cout << "\nInverse of matrix A:\n";
  132.     for(int i=0; i<n; i++) {
  133.         for(int j=0; j<n; j++)
  134.             cout << setw(8) << inv[i][j] << " ";
  135.         cout << endl;
  136.     }
  137.  
  138.     return 0;
  139. }
  140.  
Success #stdin #stdout 0s 5320KB
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stdin
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2
2 5
-3 1
11 -4
stdout
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Enter the order of square matrix: Enter coefficients of matrix A:
Enter constants of vector B:

Determinant of A: 17.0000

The solution using Cramer's Rule:
x1 = 1.8235
x2 = 1.4706

Inverse of matrix A:
  0.0588  -0.2941 
  0.1765   0.1176
https://ideone.com/cjIrWH
language:
C++ (gcc 8.3)
created:
9 days ago
visibility:
public

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