/*----------------------------------------------------------
Write the program to solve the following system of equations:
		a00x+a01y = b0
		a10x+a11y = b1
Using the determinant method
Hint: Ax = b => x=A(inverse)b
------------------------------------------------------------*/
#include <iostream>
using namespace std;

int mat_deter(double arg[2][2]) {
	int return_value =0.0 ;
	for (int n=0; n<2; ++n)
		return_value = arg[0][0]*arg[1][1] - arg[1][0]*arg[0][1];
		return return_value;
}

int main () {
	double A[2][2] = {}; // Initializing the variables
	double b[2] = {};
	double X[2] = {};
	double temp; // To hold the determinant
	double Ai[2][2] = {}; // To hold the values of inverse matrix
	cout<<"\nPlease enter the value of: a00, a01, a10 and a11 "<<endl; // Input for matrix
	cin>>A[0][0]>>A[0][1]>>A[1][0]>>A[1][1];
	cout<<"\nPlease enter the value of : b0 and b1 "<<endl; // Input for constant in RHS
	cin>>b[0]>>b[1];
	cout << "\nThe determinant of the matrix is = " << mat_deter(A) <<endl;
	temp = mat_deter(A);
	if(temp == 0)
		cout<<"\n The matrix is Singular";
	else { // Input for the inverse matrix
		cout<<"\n The inverse of the martix"<<endl;
		Ai[0][0] = (1/temp)*A[1][1];
		Ai[0][1] = (1/temp)*((-1)*A[0][1]);
		Ai[1][0] = (1/temp)*((-1)*A[1][0]);
		Ai[1][1] = (1/temp)*A[0][0];
		cout<<"\nAi[0][0]: "<<Ai[0][0]<<"\nAi[0][1]: "<<Ai[0][1]<<"\nAi[1][0]: "<<Ai[1][0]<<"\nAi[1][1]: "<<Ai[1][1];
		
		cout<<"\nMatrix Multiplication: Value of x and y"<<endl; // Multiplication of inverse with vector
		X[0] = (Ai[0][0]*b[0])+(Ai[0][1]*b[1]);
		X[1] = (Ai[1][0]*b[0])+(Ai[1][1]*b[1]);
		cout<<"\nx[0]: "<<X[0]<<"\nx[1]: "<<X[1];
	}
	return 0;
}