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  1. /*
  2. Name:Pritom Sharma
  3. Id: 230241008
  4. Report:Crsmers Rule Method
  5. */
  6.  
  7. #include <iostream>
  8. #include <iomanip>
  9. #include <vector>
  10.  
  11. using namespace std;
  12.  
  13. double determinant(vector<vector<double>> mat, int n) {
  14.     double det = 0;
  15.     if (n == 1) {
  16.         return mat[0][0];
  17.     }
  18.  
  19.     vector<vector<double>> temp(n - 1, vector<double>(n - 1));
  20.     int sign = 1;
  21.  
  22.     for (int f = 0; f < n; f++) {
  23.         int i = 0, j = 0;
  24.         for (int row = 1; row < n; row++) {
  25.             for (int col = 0; col < n; col++) {
  26.                 if (col != f) {
  27.                     temp[i][j++] = mat[row][col];
  28.                     if (j == n - 1) {
  29.                         j = 0;
  30.                         i++;
  31.                     }
  32.                 }
  33.             }
  34.         }
  35.         det += sign * mat[0][f] * determinant(temp, n - 1);
  36.         sign = -sign;
  37.     }
  38.     return det;
  39. }
  40.  
  41. void cramersRule() {
  42.     int n;
  43.     cout << "Enter the order of square matrix: ";
  44.     cin >> n;
  45.  
  46.     vector<vector<double>> A(n, vector<double>(n));
  47.     vector<double> B(n), X(n);
  48.  
  49.     cout << "Enter coefficients of matrix A:\n";
  50.     for (int i = 0; i < n; i++) {
  51.         for (int j = 0; j < n; j++) {
  52.             cin >> A[i][j];
  53.         }
  54.     }
  55.  
  56.     cout << "Enter constants of vector B: ";
  57.     for (int i = 0; i < n; i++) {
  58.         cin >> B[i];
  59.     }
  60.  
  61.     double detA = determinant(A, n);
  62.     cout << "\nDeterminant of A: " << fixed << setprecision(3) << detA << endl;
  63.  
  64.     if (detA == 0) {
  65.         cout << "Matrix is singular; the system is not uniquely solvable.\n";
  66.         return;
  67.     }
  68.  
  69.  
  70.     vector<vector<double>> invA(n, vector<double>(n));
  71.     if (n == 2) {
  72.  
  73.         invA[0][0] = A[1][1] / detA;
  74.         invA[0][1] = -A[0][1] / detA;
  75.         invA[1][0] = -A[1][0] / detA;
  76.         invA[1][1] = A[0][0] / detA;
  77.  
  78.         cout << "\nInverse of matrix A:\n";
  79.         for (int i = 0; i < n; i++) {
  80.             for (int j = 0; j < n; j++) {
  81.                 cout << fixed << setprecision(4) << invA[i][j] << "\t";
  82.             }
  83.             cout << endl;
  84.         }
  85.     }
  86.  
  87.  
  88.     vector<vector<double>> temp = A;
  89.     for (int i = 0; i < n; i++) {
  90.         for (int j = 0; j < n; j++) {
  91.             temp[j][i] = B[j];
  92.         }
  93.         X[i] = determinant(temp, n) / detA;
  94.         temp = A; // Reset temp matrix
  95.     }
  96.  
  97.     cout << "\nThe solution using Cramer's Rule:\n";
  98.     for (int i = 0; i < n; i++) {
  99.         cout << "x" << i + 1 << " = " << fixed << setprecision(6) << X[i] << endl;
  100.     }
  101. }
  102.  
  103. int main() {
  104.     cramersRule();
  105.  
  106. return 0;
  107. }
Success #stdin #stdout 0.01s 5284KB
comments (?)
stdin
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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: 58.000

Inverse of matrix A:
0.1897	0.0517	
-0.0172	0.0862	

The solution using Cramer's Rule:
x1 = -0.758621
x2 = 0.068966
https://ideone.com/y3O6Bh
language:
C++14 (gcc 8.3)
created:
7 days ago
visibility:
public

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