Multiplication of two matrices of order m*n and p*q in C++

Multiplication of matrices

The multiplication of two matrices is possible only if the number of columns in the first matrix is equal to the number of rows in the second matrix. The resulting matrix (i.e. product) will have the number of rows equal to the number of rows in the first matrix and no of columns equal to the number of column in the second matrix.

The multiplication of two matrices of order m*n and p*q is possible only if n=p and the order of resultant matrix will be m*q.

Multiplication is obtained as follows:

 MATRIX MULTIPLICATION

The ijth element of the product matrix is obtained by the summation of the product of the corresponding terms of the ith row of the first matrix and jth column of the second matrix.

Write a program in C++ to find the product of two matrices of order m*n and p*q.

In the program, we input two matrices using nested for loop in the form of a two-dimensional array. We need to check the condition required for the multiplication of two matrices. We also need to confirm that the user has entered the rows and columns of matrix smaller than the size of the array. If both conditions satisfy then the multiplication is performed and we get the result.

Program

#include<iostream.h>

#include<conio.h>

void main()

{

int a[20][20],b[20][20],c[20][20],m,n,p,q,i,j,k;

clrscr();

cout<<"Enter the number of rows in first matrix=";

cin>>m;

cout<<"Enter the number of column in first matrix=";

cin>>n;

cout<<"Enter the number of rows in second matrix=";

cin>>p;

cout<<"Enter the number of column in second matrix=";

cin>>q;

if ((n!=p)||(m>20)||(n>20)||(p>20)||(q>20))

  {

cout<<"\nInvalid input";

goto x;

}

cout<<"Input of first matrix\n";

        for(i=0;i<m;i++)

{

for(j=0;j<n;j++)

{

cout<<"Enter the element of["<<i<<"]["<<j<<"]= ";

cin>>a[i][j];

}

}

cout<<"Input of second matrix\n";
        for(i=0;i<p;i++)

{
for(j=0;j<q;j++)

{

cout<<"Enter the element of["<<i<<"]["<<j<<"]= ";

cin>>b[i][j];

}

}

for(i=0;i<m;i++)                                                                                   //Multiplication of matrix

{

for(j=0;j<q;j++)

{

c[i][j]=0;

for(k=0;k<n;k++)

{

c[i][j]=c[i][j]+a[i][k]*b[k][j];

}

}

}

cout<<"\nYour output matrix\n\n";

         for(i=0;i<m;i++)

{

for(j=0;j<q;j++)

{

cout<<c[i][j]<<"\t";

}

cout<<endl;

}

x:getch();

}

Output

MATRIX MULTIPLICATION

Explanation

In the program we are performing multiplication of two matrix of order 3*2 and 2*3. The input of is taken as shown above. The multiplication is calculated as shown below:

i<3          j<3          k<2          c[i][j]          c[i][j]=c[i][j]+a[i][k]*b[k][j]

0             0              0               0               c[0][0]=c[0][0]+a[0][0]*b[0][0]=0+1*5=5

                               1               5               c[0][0]=c[0][0]+a[0][1]*b[1][0]=5+3*4=17      

               1              0               0               c[0][1]=c[0][1]+a[0][0]*b[0][1]=0+1*3=3 

                               1               3               c[0][1]=c[0][1]+a[0][1]*b[1][1]=3+3*2=9  

               2              0               0               c[0][2]=c[0][2]+a[0][0]*b[0][2]=0+1*5=5 

                               1               5               c[0][2]=c[0][2]+a[0][1]*b[1][2]=5+3*6=23.

The process continues till i=2 and calculates all elements of product matrix of order 3*3. We obtain the result and it is printed on the screen. 

Introduction to matrix and types of array

Matrix and array

Matrix

Matrix is a rectangular array of numbers arranged in rows (horizontal lines) and columns (vertical lines) enclosed between a pair of round or square brackets. E.g.

EXAMPLES OF MATRIX

Order of matrix

Order or size of a matrix is given by the number of rows followed by the number of columns. In the example the first matrix has one row and two columns, so the order is 1*2 (read as 1 by 2). Similarly, the order of other matrices is 2*2, 3*3, 3*1.

Array

An array is a homogeneous (same type) collection of elements or data having a common property and sharing a common name. It can be declared normally like ordinary variables using [ ] for size specification.

For e.g. int a[5] is used to store 5 integer values in a[0],a[1],a[2],a[3],a[4].

a[0] is first element of array a. a[0],a[1],a[2],a[3],a[4] are called elements or subscripts.

All 5 variables are stored in different memory locations.

Types of array 

Single dimensional array

                                           The array having only a single pair of brackets with array name is called single dimensional array. They have single size specification.E.g. a[5].

Multidimensional array

                                         The array having more than one pair of brackets with the array name is called a multidimensional array. They have multiple size specification.

E.g. ex[5][5], g[2][4][2].

           

A two-dimensional array is an array having a pair of square brackets(or having two dimensions). It is an example of multidimensional array. It has a double size specification. A two-dimensional array is used for the implementation of a matrix. When a two-dimensional array is implemented as a matrix, the first dimension represents the number of rows and the second dimension represents the number of columns. E.g. a[2][2], a[3][2], a[4][4].

An array a[2][2] will have four elements which are a[0][0], a[0][1], a[1][0], a[1][1].