#include<iostream>
#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])
{
cout.precision(3);
cout.setf(ios::fixed);
// 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);
cout<<" \n\n \t Determinant of the Equation \n\n";
cout<<"\t general determinant = "<<D<<"\n\n";
cout<<"\t x1 determinant = "<<D1<<"\n\n";
cout<<"\t x2 determinant = "<<D2<<"\n\n";
cout<<"\t x3 determinant = "<<D3<<"\n\n";
// 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
cout<<"\n\n \t Result of the simultanous Equation \n\n";
cout<<"\t x1 = "<<x<<"\n\n";
cout<<"\t x2 = "<<y<<"\n\n";
cout<<"\t x3 = "<<z<<"\n\n";
}
// Case 2
else {
if (D1 == 0 && D2 == 0 && D3 == 0)
cout<<"Infinite solutions\n";
else if (D1 != 0 || D2 != 0 || D3 != 0)
cout<<"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 },
// };
double equation[3][4];
for(int i=0; i<3; i++){
cout<<"Enter Equation "<<i+1<<"\n\n";
for(int j=0; j<4; j++)
{
//Input values of equations in rows and column ;
cout<<"enter values for row :"<<i+1<<" and column : "<<j+1<<"\n";
cin>>equation[i][j];
}
}
//display the equation
cout<<"\n\n Matrix representation of the equation \n";
for(int i=0; i<3; i++){
for(int j=0; j<4; j++){
cout<<"\t"<<equation[i][j]<<" ";
}
cout<<"\n\n";
}
findSolution(equation);
return 0;
}
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C++ is a widely used middle-level programming language.
When ever you want to perform a set of operations based on a condition If-Else is used.
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