Array Exercises
Write a C program to read elements in a matrix and find determinant of the given matrix. C program to find determinant of a 2x2 matrix and 3x3 matrix. Logic to find determinant of a matrix in C programming.
Required knowledge
Basic C programming, C for loop, ArrayS
What is determinant?
The Determinant of a matrix is a special number that can be calculated from the elements of a square matrix. The determinant of a matrix A is denoted by det (A), det A or |A|.
Program to calculate determinant of 2x2 matrix
/**
* C program to find determinant of 2x2 matrix
*/
#include <stdio.h>
#define SIZE 2 // Matrix size
int main()
{
int A[SIZE][SIZE];
int row, col;
long det;
/* Input elements in matrix A from user */
printf("Enter elements in matrix of size 2x2: \n");
for(row=0; row<SIZE; row++)
{
for(col=0; col<SIZE; col++)
{
scanf("%d", &A[row][col]);
}
}
/*
* det(A) = ad - bc
* a = A[0][0], b = A[0][1], c = A[1][0], d = A[1][1]
*/
det = (A[0][0] * A[1][1]) - (A[0][1] * A[1][0]);
printf("Determinant of matrix A = %ld", det);
return 0;
}
Output
Enter elements in matrix of size 2x2:
10 20
30 40
Determinant of matrix A = -200
Process returned 0 (0x0) execution time : 7.827 s
/**
* C program to find determinant
*/
#include <stdio.h>
int main()
{
int A[10][10];
int row, col;
long det,m;
printf("Enter size of matrix:");
scanf("%d",&m);
/* Input elements in matrix A from user */
printf("Enter elements in matrix: \n");
for(row=0; row<m; row++)
{
for(col=0; col<m; col++)
{
scanf("%d", &A[row][col]);
}
}
/*
* det(A) = ad - bc
* a = A[0][0], b = A[0][1], c = A[1][0], d = A[1][1]
*/
det = (A[0][0] * A[1][1]) - (A[0][1] * A[1][0]);
printf("Determinant of matrix A = %ld", det);
return 0;
}
Output:
Enter size of matrix:2
Enter elements in matrix:
9 8
7 6
Determinant of matrix A = -2
Process returned 0 (0x0) execution time : 9.954 s
Program to calculate determinant of 3x3 matrix
/**
* C program to find determinant of 3x3 matrix
*/
#include <stdio.h>
#define SIZE 3 // Matrix size
int main()
{
int A[SIZE][SIZE];
int row, col;
int a, b, c, d, e, f, g, h, i;
long det;
/* Input elements in matrix A from user */
printf("Enter elements in matrix of size 3x3: \n");
for(row=0; row<SIZE; row++)
{
for(col=0; col<SIZE; col++)
{
scanf("%d", &A[row][col]);
}
}
/*
* Used as a temporary variables to make calculation easy
* | |
* | a b c |
* | d e f |
* | g h i |
* | |
*/
a = A[0][0];
b = A[0][1];
c = A[0][2];
d = A[1][0];
e = A[1][1];
f = A[1][2];
g = A[2][0];
h = A[2][1];
i = A[2][2];
/*
* det(A) = a(ei - fh) - b(di - fg) + c(dh - eg)
*/
det = (a*(e*i - f*h)) - (b*(d*i - f*g)) + (c*(d*h - e*g));
printf("Determinant of matrix A = %ld", det);
return 0;
}
Note: You can also calculate determinants without using additional temporary variables a, b, c, d, e, f, g, h, u. These variable are only used to make the program simple to use. You can directly use A[0][0] for a etc.
