Matrix Multiplication

 Matrix Multiplication

First be Know that What is matrix  A set of mn number (real or imaginary) arranged in the form of rectangular array of m rows and n columns is called m x n matrix  (to be read as ‘m by n’ matrix).

Matrix Multiplication

Let us first define the product of a row matrix and a column matrix.

Let  A= [a1, a2,  a3 …….. an] be a row matrix and  B =    b1         be a column matrix. Then , we define                                                                  b2 …                                                                                                                                      bn                                                                            A*B = a1b1 + a2b2 + a3b3 + …………….. + anbn.

Definition : Two matrices A and B are conformable for the product AB if the number of column in A (pre-multiplier) is same as the number of row in B(post-multipier).

On other word Column of matrix A is equal to Row of matrix B When result is matrix Row of matrix A and column of matrix B.

 

= 1*3 + 2*4 + 3*5 and similarly others. than the multiplication of the matrix is order(3 x 2) .

 

Program of Matrix Multiplication shown below :

// program for multiplication of two matrices.

#include<stdio.h>

#include<conio.h>

#define ROW1 3

#define COL1 3

#define ROW2 COL1

#define COL2 2

int main()

{

    int A[ROW1][COL1],B[ROW2][COL2],C[ROW1][COL2];

    int x,y,z;

    printf("Enter matrix A(%dx%d) Row-wise:\n",ROW1,COL1);

    for(x=0;x<ROW1;x++)

    {

        for(y=0;y<COL1;y++)

        {

            scanf("%d",&A[x][y]);

        }

    }

    printf("Enter matrix B(%dx%d) Row-wise:\n",ROW2,COL2);

    for(x=0;x<ROW2;x++)

    {

        for(y=0;y<COL2;y++)

        {

            scanf("%d",&B[x][y]);

        }

    }

    // Multiplication.

    for(x=0;x<ROW1;x++)

    {

        for(y=0;y<COL2;y++)

        {

            C[x][y]=0;

            for(z=0;z<COL1;z++)

            {

                C[x][y]+=A[x][z]*B[z][y]; //matrix multiply and add;

            }

        }

    }

    printf("multiplication of matrix A and  B is \n");

    for(x=0;x<ROW1;x++)

    {

        for(y=0;y<COL2;y++)

        {

            printf("%d\t",C[x][y]);

        }

        printf("\n");

    }

    return 0;

}

Output :

Enter matrix A(3x3) Row-wise: 1 2 3 4 5 6 7 8 9 Enter matrix B(3x2) Row-wise: 3 2 4 5 5 6yo multiplication of matrix A and B is 26 30 62 69 98 108

Thank you