Home » C++ programs

Representing System of Linear Equations using Matrix

Here, we are going to learn about Representing System of Linear Equations using Matrix.
Submitted by Raja Sethupathi V, on January 28, 2019

A Linear Equation can be represented in matrix form using a:

• Coefficient Matrix
• Variable Matrix and
• Constant Matrix

The System of linear equation in three variables,

a1x+b1y+c1z=d1
a2x+b2y+c2z=d2
a3x+b3y+c3z=d3

The Matrix Representation would be

a1 b1 c1       xd1
a2 b2 c2y      =d2
a3 b3 c3 zd3

We generalize the result of n variable

a1 b1 c1             
a2 b2 c2     __     Coefficient Matrix
a3 b3 c3
x,y,z  are Variable Matrix
d1,d2,d3 are Constant Matrix

Consider the System,

x+2y+3z=4
5x+6y+7z=8
8x+7y+6z=5

Then, the coefficient matrix for the above system is

1 2 3 
5 6 7 
8 7 6

Variable Matrix are X, Y, Z

Constant Matrix are 4,8,5

Representing of linear Matrix in above System is:

1 2 3 x     4
5 6 7 y     = 8
8 7 6 z     5

C++ program to implement the Representation of Linear Equation in Matrix form

#include <iostream>
using namespace std;

int main()
{
	cout<< "Enter the number of variables in the equations: ";
	int n;
	
	cin>>  n;
	char var = 'x';
	int a[n][n],b[n][1];
	
	for (int i = 0; i< n; i++)
	{
		for (int j = 0; j < n; j++)
		{
			cin>> a[i][j];   //Get the Matrix values
		}
		cin>> b[i][0]; //Get the constant values
	}
	
	cout<< "\nLinear Equation in Matrix representation is: \n";
	for (int i = 0; i< n; i++)
	{
		for (int j = 0; j < n; j++)
		{
			cout<<" "<< a[i][j]; //print the matrix values
		}
		//print the variable and constant values
		cout<< "  " <<static_cast<char>(var) << "  =  " << b[i][0]<< "\n";
		var++;
	}
	
	return 0;
}

Output

Enter the number of variables in the equations:
3
1 2 3 4
5 6 7 8
8 7 6 5
Linear Equation in Matrix representation is: 
1 2 3 x   =    4
5 6 7 y   = 8
8 7 6 z   =   5

Applications:

Systems of Linear Equations can be used to solve some Real – Time Problems:

• Solving a Mixture problems
• Distance Rate Time problems
• Business Based Problems