Example: Inverse of a 2x2 Matrix using Adjoint Method in C++

// Inverse of a 2x2 Matrix using Adjoint Method
#include <iostream>
#include <vector>
#include <iomanip> // For std::fixed and std::setprecision

using namespace std;

// Function to calculate the determinant of a 2x2 matrix
double determinant2x2(const vector<vector<double>>& matrix) {
    return matrix[0][0] * matrix[1][1] - matrix[0][1] * matrix[1][0];
}

int main() {
    // Step 1: Define the 2x2 matrix
    vector<vector<double>> matrix = {
        {3, 4},
        {1, 2}
    };

    cout << "Original Matrix:" << endl;
    for (const auto& row : matrix) {
        for (double val : row) {
            cout << val << " ";
        }
        cout << endl;
    }
    cout << endl;

    // Step 2: Calculate the determinant
    double det = determinant2x2(matrix);

    if (det == 0) {
        cout << "Determinant is 0. Inverse does not exist." << endl;
        return 0;
    }

    // Step 3: Calculate the adjoint matrix (for a 2x2 matrix, this is simpler)
    // adj(A) = | d  -b |
    //          | -c  a |
    // where A = | a  b |
    //           | c  d |
    vector<vector<double>> adjoint(2, vector<double>(2));
    adjoint[0][0] = matrix[1][1];
    adjoint[0][1] = -matrix[0][1];
    adjoint[1][0] = -matrix[1][0];
    adjoint[1][1] = matrix[0][0];

    // Step 4: Calculate the inverse matrix
    vector<vector<double>> inverse(2, vector<double>(2));
    double inv_det = 1.0 / det;

    for (int i = 0; i < 2; ++i) {
        for (int j = 0; j < 2; ++j) {
            inverse[i][j] = inv_det * adjoint[i][j];
        }
    }

    // Step 5: Print the inverse matrix
    cout << "Inverse Matrix:" << endl;
    cout << fixed << setprecision(2); // Format output to 2 decimal places
    for (const auto& row : inverse) {
        for (double val : row) {
            cout << val << " ";
        }
        cout << endl;
    }

    return 0;
}