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  1. /*
  2. Name: Anuska Alam
  3. Id: 230241021
  4. Report: Cramer's rule
  5. */
  6. #include <bits/stdc++.h>
  7. using namespace std;
  8.  
  9. // 2x2 determinant
  10. float det2x2(float m[2][2]) {
  11.     return m[0][0]*m[1][1] - m[0][1]*m[1][0];
  12. }
  13.  
  14. // 3x3 determinant
  15. float det3x3(float m[3][3]) {
  16.     return m[0][0]*(m[1][1]*m[2][2] - m[1][2]*m[2][1])
  17.          - m[0][1]*(m[1][0]*m[2][2] - m[1][2]*m[2][0])
  18.          + m[0][2]*(m[1][0]*m[2][1] - m[1][1]*m[2][0]);
  19. }
  20.  
  21. int main() {
  22.     int n;
  23.     cout << "Enter order of square matrix (2 or 3): ";
  24.     cin >> n;
  25.  
  26.     if (n != 2 && n != 3) {
  27.         cout << "Only 2x2 or 3x3 matrices are supported.\n";
  28.         return 0;
  29.     }
  30.  
  31.     float A[3][3] = {0}, B[3] = {0}; // initialized to 0
  32.  
  33.     cout << "Enter coefficients of matrix A:\n";
  34.     for (int i = 0; i < n; i++)
  35.         for (int j = 0; j < n; j++)
  36.             cin >> A[i][j];
  37.  
  38.     cout << "Enter constants of vector B:\n";
  39.     for (int i = 0; i < n; i++)
  40.         cin >> B[i];
  41.  
  42.     cout << fixed << setprecision(3);
  43.  
  44.     if (n == 2) {
  45.         float matA[2][2] = {
  46.             {A[0][0], A[0][1]},
  47.             {A[1][0], A[1][1]}
  48.         };
  49.  
  50.         float detA = det2x2(matA);
  51.         cout << "\nDeterminant of A: " << detA << endl;
  52.         if (detA == 0) {
  53.             cout << "Matrix is singular; not uniquely solvable.\n";
  54.             return 0;
  55.         }
  56.  
  57.         float A1[2][2] = {{B[0], A[0][1]}, {B[1], A[1][1]}};
  58.         float A2[2][2] = {{A[0][0], B[0]}, {A[1][0], B[1]}};
  59.  
  60.         float x1 = det2x2(A1) / detA;
  61.         float x2 = det2x2(A2) / detA;
  62.  
  63.         cout << "\nThe solution using Cramer's Rule:\n";
  64.         cout << "x1 = " << x1 << endl;
  65.         cout << "x2 = " << x2 << endl;
  66.  
  67.     } else if (n == 3) {
  68.         float detA = det3x3(A);
  69.         cout << "\nDeterminant of A: " << detA << endl;
  70.         if (detA == 0) {
  71.             cout << "Matrix is singular; not uniquely solvable.\n";
  72.             return 0;
  73.         }
  74.  
  75.         float A1[3][3], A2[3][3], A3[3][3];
  76.         for (int i = 0; i < 3; i++) {
  77.             A1[i][0] = B[i]; A1[i][1] = A[i][1]; A1[i][2] = A[i][2];
  78.             A2[i][0] = A[i][0]; A2[i][1] = B[i]; A2[i][2] = A[i][2];
  79.             A3[i][0] = A[i][0]; A3[i][1] = A[i][1]; A3[i][2] = B[i];
  80.         }
  81.  
  82.         float x1 = det3x3(A1) / detA;
  83.         float x2 = det3x3(A2) / detA;
  84.         float x3 = det3x3(A3) / detA;
  85.  
  86.         cout << "\nThe solution using Cramer's Rule:\n";
  87.         cout << "x1 = " << x1 << endl;
  88.         cout << "x2 = " << x2 << endl;
  89.         cout << "x3 = " << x3 << endl;
  90.     }
  91.  
  92.     return 0;
  93. }
Success #stdin #stdout 0s 5320KB
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stdin
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3
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2 3 5
4 0 5

5 8 2
stdout
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Enter order of square matrix (2 or 3): Enter coefficients of matrix A:
Enter constants of vector B:

Determinant of A: 13.000

The solution using Cramer's Rule:
x1 = 3.000
x2 = 4.000
x3 = -2.000
https://ideone.com/mQe16y
language:
C++ (gcc 8.3)
created:
6 days ago
visibility:
public

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