// CPP program to calculate solutions of linear
// equations using cramer's rule
#include <bits/stdc++.h>
using namespace std;
// This functions finds the determinant of Matrix
double determinantOfMatrix(double mat[3][3])
{
double ans;
ans = mat[0][0] * (mat[1][1] * mat[2][2] - mat[2][1] * mat[1][2])
- mat[0][1] * (mat[1][0] * mat[2][2] - mat[1][2] * mat[2][0])
+ mat[0][2] * (mat[1][0] * mat[2][1] - mat[1][1] * mat[2][0]);
return ans;
}
// This function finds the solution of system of
// linear equations using cramer's rule
void findSolution(double coeff[3][4])
{
// Matrix d using coeff as given in cramer's rule
double d[3][3] = {
{ coeff[0][0], coeff[0][1], coeff[0][2] },
{ coeff[1][0], coeff[1][1], coeff[1][2] },
{ coeff[2][0], coeff[2][1], coeff[2][2] },
};
// Matrix d1 using coeff as given in cramer's rule
double d1[3][3] = {
{ coeff[0][3], coeff[0][1], coeff[0][2] },
{ coeff[1][3], coeff[1][1], coeff[1][2] },
{ coeff[2][3], coeff[2][1], coeff[2][2] },
};
// Matrix d2 using coeff as given in cramer's rule
double d2[3][3] = {
{ coeff[0][0], coeff[0][3], coeff[0][2] },
{ coeff[1][0], coeff[1][3], coeff[1][2] },
{ coeff[2][0], coeff[2][3], coeff[2][2] },
};
// Matrix d3 using coeff as given in cramer's rule
double d3[3][3] = {
{ coeff[0][0], coeff[0][1], coeff[0][3] },
{ coeff[1][0], coeff[1][1], coeff[1][3] },
{ coeff[2][0], coeff[2][1], coeff[2][3] },
};
// Calculating Determinant of Matrices d, d1, d2, d3
double D = determinantOfMatrix(d);
double D1 = determinantOfMatrix(d1);
double D2 = determinantOfMatrix(d2);
double D3 = determinantOfMatrix(d3);
printf("D is : %lf \n", D);
printf("D1 is : %lf \n", D1);
printf("D2 is : %lf \n", D2);
printf("D3 is : %lf \n", D3);
// Case 1
if (D != 0) {
// Coeff have a unique solution. Apply Cramer's Rule
double x = D1 / D;
double y = D2 / D;
double z = D3 / D; // calculating z using cramer's rule
printf("Value of x is : %lf\n", x);
printf("Value of y is : %lf\n", y);
printf("Value of z is : %lf\n", z);
}
// Case 2
else {
if (D1 == 0 && D2 == 0 && D3 == 0)
printf("Infinite solutions\n");
else if (D1 != 0 || D2 != 0 || D3 != 0)
printf("No solutions\n");
}
}
// Driver Code
int main()
{
// storing coefficients of linear equations in coeff matrix
double coeff[3][4] = {
{ 2, -1, 3, 9 },
{ 1, 1, 1, 6 },
{ 1, -1, 1, 2 },
};
findSolution(coeff);
return 0;
}
