Operations on Two-Dimensional Arrays

OPERATIONS ON TWO-DIMENSIONAL ARRAYS

Two-dimensional arrays can be used to implement the mathematical concept of matrices. In mathematics, a matrix is a grid of numbers, arranged in rows and columns. Thus, using two-dimensional arrays, we can perform the following operations on an m x n matrix.

Transpose Transpose of a m x n matrix A is given as a n x m matrix B where,

B_i,j = A_j,i

Sum Two matrices that are compatible with each other can be added together thereby storing the result in the third matrix. Two matrices are said to be compatible when they have the same number of rows and columns. Elements of the matrices can be added by writing:

C_i,j = A_i,j + B_i,j

Difference Two matrices that are compatible with each other can be subtracted thereby storing the result in the third matrix. Two matrices are said to be compatible when they have the same number of rows and columns. Elements of the matrices can be subtracted by writing:

C_i,j = A_i,j - B_i,j

Product Two matrices can be multiplied with each other if the number of columns in the first matrix is equal to the number of rows in the second matrix. Therefore, m x n matrix A can be multiplied with a p x q matrix if n = P. Elements of the matrices can be multiplied by writing:

C_i,j = Σ A_i,k B_k,j for k=1 to k < n

27. Write a program to read and display a 3 x 3 matrix.

#include <stdio.h>

#include <conio.h>

int main()

int i, j, mat [3] [3];

clrscr();

printf("\n Enter the elements of the matrix ");

printf("\n *****************************");

for (i=0; i<3; i++)

{

for(j=0;j<3;j++)

scanf("%d", &mat [i] [j]);

}

printf("\n The elements of the matrix are ");

printf("\n **************************");

for (i=0; i<3;i++)

{

printf("\n");

for (j=0;j<3;j++)

printf("\t%d", mat [i] [j]);

}

return 0;

}

Output

Enter the elements of the matrix

************************

1 2 3 4 5 6 7 8 9

The elements of the matrix are

************************

1 2 3

4 5 6

7 8 9

28. Write a program to transpose a 3 x 3 matrix.

#include <stdio.h>

#include <conio.h>

int main()

{

int i, j, mat [3] [3], transposed_mat [3] [3];

clrscr();

printf("\n Enter the elements of the matrix");

printf("\n ********************");

for (i=0;i<3; i++)

{

for(j=0;j<3;j++)

{

scanf("%d", &mat [i][j]);

}

}

printf("\n The elements of the matrix are ");

printf("\n ********************");

for (i=0;i<3; i++)

{

printf("\n");

for(j=0;j<3;j++)

printf("\t%d", mat [i] [j]);

}

for (i=0; i<3; i++)

{

for(j=0;j<3;j++)

transposed_mat [i][j] = mat [j] [i];

}

printf("\n The elements of the transposed matrix are are ");

printf("\n ***********************");

for (i=0;i<3; i++)

{

printf("\n");

for(j=0;j<3;j++)

printf("\t%d", transposed_ mat [i] [j]);

}

return 0;

}

Output

Enter the elements of the matrix

***********************

1 2 3 4 5 6 7 8 9

The elements of the matrix are

***********************

1 2 3

4 5 6

7 8 9

The elements of the transposd matrix are

***********************

1 4 7

2 5 8

7 8 9

29. Write a program to input two m x n matrices and then calculate the sum of their corresponding elements and store it in a third m x n matrix.

#include <stdio.h>

#include <conio.h>

int main()

{

int i, j;

int rowsl, colsl, rows2, cols2, rows_sum, cols_sum;

int mat1 [5] [5], mat2 [5] [5], sum [5] [5];

clrscr();

printf("\n Enter the number of rows in the first matrix: ");

scanf("%d", &rows1);

printf("\n Enter the number of columns in the first matrix: ");

scanf("%d", &cols1);

printf("\n Enter the number of rows in the second matrix: ");

 or scanf("%d", &rows2);

printf("\n Enter the number of columns in br the second matrix: ");

scanf("%d", &cols2);

if (rowsl != rows2 || cols1 != cols2)

{

printf("\n The number of rows and columns of both the matrices must be equal");

getch();

exit();

}

rows_sum = rowsl;

cols_sum = cols1;

printf("\n Enter the elements of the first matrix");

printf("\n ***********************");

for (i=0;i<rowsl;i++)

{

for(j=0;j<cols1;j++)

scanf("%d", &mat1 [i] [j]);

printf("\n Enter the elements of the second matrix");

printf("\n ***********************");

for (i=0; i<rows2; i++)

{

for(j=0;j<cols2;j++)

scanf("%d", &mat2 [i] [j]);

}

for (i=0;i<rows_sum; i++)

{

for (j=0;j<cols_sum, j++)

sum [i] [j] = mat1 [i] [j] + mat2 [i] [j];

printf("\n The elements of the resultant matrix are");

printf("\n ***********************");

for (i=0;i<rows_sum; i++)

{

printf("\n");

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

printf("\t%d", sum [i][j]);

}

return 0;

}

Output

Enter the number of rows in the first matrix: 2

Enter the number of columns in the first matrix: 2

Enter the number of rows in the second matrix: 2

Enter the number of columns in the second matrix: 2

Enter the elements of the first matrix

**************************

1 2 3 4

Enter the elements of the second matrix

***************************

5 6 7 8

The elements of the resultant matrix are

******************************

6    8

10 12

30. Write a program to multiply two m x n matrices.

#include <stdio.h>

#include <conio.h>

int main()

{

int i, j, k;

int rowsl, colsl, rows2, cols2, res_rows, res_cols;

int mat1 [5] [5], mat2 [5] [5], res [5] [5];

clrscr();

printf("\n Enter the number of rows in the first matrix: ");

scanf("%d", &rows1);

printf("\n Enter the number of columns in the first matrix: ");

scanf("%d", &cols1);

printf("\n Enter the number of rows in the second matrix: ");

scanf("%d", &rows2);

printf("\n Enter the number of columns in the second matrix: ");

scanf("%d", &cols2);

if (colsl != rows2)

{

printf("\n The number of columns in the first matrix must be equal to the number of rows in the second matrix");

getch();

exit();

}

res_rows = rows1;

res cols = cols2;

printf("\n Enter the elements of the first matrix");

printf("\n **************************");

for (i=0;i<rowsl; i++)

{

for(j=0;j<cols1;j++)

scanf("%d", &mat1 [i] [j]);

}

printf("\n Enter the elements of the second matrix");

printf("\n ****************************");

for (i = 0; i < rows2; i++)

{

for (j = 0; j < cols2; j++)

scanf("%d",&mat2 [i] [j]);

}

for (i = 0; i < res_ rows; i++)

{

j=0;

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

{

res [i] [j]=0;

for (k 0; k < res_cols; k++)

res [i] [j] += mat1 [i] [k] * mat2 [k] [j];

}

}

printf("\n The elements of the product matrix are");

printf("\n ****************************");

for (i=0;i<res_rows; i++)

{

printf("\n");

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

printf("\t %d", res [i] [j]);

}

return 0;

}

Output

Enter the number of rows in the first matrix: 2

Enter the number of columns in the first matrix: 2

Enter the number of rows in the second matrix: 2

Enter the number of columns in the second matrix: 2

Enter the elements of the first matrix

***********************

1 2 3 4

Enter the elements of the second matrix

***********************

5 6 7 8

The elements of the product matrix are

************************

19 22

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