### DataStructure Program for matrix operations dertminant, singular

#include <stdio.h>
#include <conio.h>
#include <math.h>
#define MAX 3
void matrix ( int [3][3] ) ;
void create ( int [3][3] ) ;
void display ( int [3][3] ) ;
void matmul ( int [3][3], int [3][3], int [3][3] ) ;
void transpose ( int [3][3], int [3][3] ) ;
int determinant ( int [3][3] ) ;
int isortho ( int [3][3] ) ;
void main( )
{
int mat [3][3], d ;
clrscr( ) ;
printf ( "\nEnter elements for array: \n\n" ) ;
create ( mat ) ;
printf ( "\nThe Matrix: \n" ) ;
display ( mat ) ;
d = determinant ( mat ) ;
printf ( "\nThe determinant for given matrix: %d.\n", d ) ;
if ( d == 0 )
printf ( "\nMatrix is singular.\n" ) ;
else
printf ( "\nMatrix is not singular.\n" ) ;
d = isortho ( mat ) ;
if ( d != 0 )
printf ( "\nMatrix is orthogonal.\n" ) ;
else
printf ( "\nMatrix is not orthogonal.\n" ) ;
getch( ) ;
}
/* initializes the matrix mat with 0 */
void matrix ( int mat[3][3] )
{
int i, j ;
for ( i = 0 ; i < MAX ; i++ )
{
for ( j = 0 ; j < MAX ; j++ )
mat[i][j] = 0 ;
}
}
/* creates matrix mat */
void create ( int mat[3][3] )
{
int n, i, j ;
for ( i = 0 ; i < MAX ; i++ )
{
for ( j = 0 ; j < MAX ; j++ )
{
printf ( "Enter the element: " ) ;
scanf ( "%d", &n ) ;
mat[i][j] = n ;
}
}
}
/* displays the contents of matrix */
void display ( int mat[3][3] )
{
int i, j ;
for ( i = 0 ; i < MAX ; i++ )
{
for ( j = 0 ; j < MAX ; j++ )
printf ( "%d\t", mat[i][j] ) ;
printf ( "\n" ) ;
}
}
/* multiplies two matrices */
void matmul ( int mat1[3][3], int mat2[3][3], int mat3[3][3] )
{
int i, j, k ;
for ( k = 0 ; k < MAX ; k++ )
{
for ( i = 0 ; i < MAX ; i++ )
{
mat3[k][i] = 0 ;
for ( j = 0 ; j < MAX ; j++ )
mat3[k][i] += mat1[k][j] * mat2[j][i] ;
}
}
}
/* obtains transpose of matrix m1 */
void transpose ( int mat[3][3], int m[3][3] )
{
int i, j ;
for ( i = 0 ; i < MAX ; i++ )
{
for ( j = 0 ; j < MAX ; j++ )
m[i][j] = mat[j][i] ;
}
}
/* finds the determinant value for given matrix */
int determinant( int mat[3][3] )
{
int sum, i, j, k, p ;
sum = 0 ; j = 1 ; k = MAX - 1 ;
for ( i = 0 ; i < MAX ; i++ )
{
p = pow ( -1, i ) ;
if ( i == MAX - 1 )
k = 1 ;
sum = sum + ( mat[0][i] * ( mat[1][j] * mat[2][k] - mat[2][j] * mat[1][k] ) ) * p ; j = 0 ;
}
return sum ;
}
/* checks if given matrix is an orthogonal matrix */
int isortho ( int mat[3][3] )
{
/* transpose the matrix */
int m1[3][3], m2[3][3], i ;
transpose ( mat, m1 ) ;
/* multiply the matrix with its transpose */
matmul ( mat, m1, m2 ) ;
/* check for the identity matrix */
for ( i = 0 ; i < MAX ; i++ )
{
if ( m2[i][i] == 1 )
continue ;
else
break ;
}
if ( i == MAX )
return 1 ;
else
return 0 ;
}