Multiplication of Matrices - concept, program code

In my previous posts, I had briefed about two basic functions that can be performed on a 2 Dimension (2D array, commonly known as matrix) - Addition of two matrices and subtracting one matrix from the other.

In this post I will be discussing the concept of Multiplication of 2 matrices and show you an implementation of the same using a C++ program code.

Concept / Algorithm :

Before proceeding we must keep in mind the basic rule of matrix multiplication which is explained as follows:

Consider a matrix A of dimensions m x n, which is to be multiplied with matrix B of size p x q. Multiplication of matrix A with B is possible if and only if m = q. The dimension of the resultant matrix thus formed will be n x p. (The two matrices can be a square matrix each)

If the condition m = q is satisfied, multiply each consecutive column of the matrix A with each rows of the matrix B one after the other. The result gets stored in the corresponding intersecting location. Look on for the example below to get a clear vision on the concept.

Example :

The example below illustrated the multiplication of two matrices. Matrix A has dimension of 2x3 and Matrix B is of 3x2.

(1, 2, 3) • (7, 9, 11) = 1×7 + 2×9 + 3×11 = 58

(1, 2, 3) • (8, 10, 12) = 1×8 + 2×10 + 3×12 = 64

(4, 5, 6) • (7, 9, 11) = 4×7 + 5×9 + 6×11 = 139

(4, 5, 6) • (8, 10, 12) = 4×8 + 5×10 + 6×12 = 154

Running Program Code :

#include<iostream.h>
#include<process.h>
#include<iomanip.h>
#include<conio.h>
const int max=10;
void main()
{
 clrscr();
 char ch;
 int A[max][max],B[max][max],C[max][max],n,m,p,q,i,j,k;
 cout<<"\n\n\t\tTHIS WILL MULTIPLY TWO MATRICES\t\t\n"<<endl;
 cout<<"\n\nFor multipling two matrices, both should be square matrix 

\n and of equal dimension\n"<<endl;
 do
 {
  cout<<"\nEnter dimensions of first matrix : \n";
  cout<<"\n\nNumber of ROWS : ";
  cin>>m;
  cout<<"\n\nNumber of COLUMNS :";
  cin>>n;
  if(m>max || n>max)
  cout<<"\n\nEnter dimension less than "<<max;
 }
 while(m>max || n>max);
 cout<<endl<<endl;
 do
 {
  cout<<"\nEnter dimensions of second matrix : \n";
  cout<<"\n\nNumber of ROWS : ";
  cin>>p;
  cout<<"\n\nNumber of COLUMNS :";
  cin>>q;
  if(p>max || q>max)
  cout<<"\n\nEnter dimension less than "<<max;
 }
 while(p>max || q>max);
 if(n==p)
 {
  cout<<endl<<endl;
  cout<<"\n\nEnter the FIRST matix (row wise) : "<<endl;
  for(i=0; i<m; ++i)
  {
   for(j=0; j<n; ++j)
   {
   cout<<"\nElement at position ["<<i<<"]["<<j<<"] :  ";
    cin>>A[i][j];
   }
  }
  cout<<"\n\nThe FIRST matrix is : \n\n";
  for(i=0; i<m; ++i)
  {
   cout<<"\n\t\t";
   for(j=0; j<n; ++j)
   {
    cout<<setw(5)<<A[i][j];
   }
   cout<<"\n\n";
  }
  cout<<endl;
  cout<<"\n\nEnter the SECOND matix (row wise) : "<<endl;
  for(i=0; i<p; ++i)
  {
   for(j=0; j<q; ++j)
   {
   cout<<"\nElement at position ["<<i<<"]["<<j<<"] :  ";
    cin>>B[i][j];
   }
  }
  cout<<"\n\nThe SECOND matrix is : \n\n";
  for(i=0; i<p; ++i)
  {
   cout<<"\n\t\t";
   for(j=0; j<q; ++j)
   {
    cout<<setw(5)<<B[i][j];
   }
   cout<<"\n\n";
  }
  cout<<endl;
  for(i=0; i<m; ++i)
  {
   cout<<"\n";
   for(j=0; j<q; ++j)
   {
    C[i][j]=0;
    for(int k=0; k<n; ++k)
    C[i][j]=C[i][j]+A[i][k]*B[k][j];
   }
  }
  cout<<"\n\nThe product is : ";
  for(i=0; i<m; ++i)
  {
   cout<<"\n\t\t";
   for(j=0; j<q; ++j)
   {
    cout<<setw(7)<<C[i][j];
   }
   cout<<"\n\n";
  }
 }
 else
  cout<<"\n\nSorry!!!! Product not possible";

 getch();
}

Thanks for reading the post…If you have any query regarding the concept or the program code, mention it in the comment below or ask us on Facebook or Google Plus.