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C Program to find Determinant of a Matrix

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How to write a C Program to find Determinant of a Matrix with example. Below image will show you the mathematical formula behind this program

C Program to find Determinant of a Matrix 0

C Program to find Determinant of a Matrix – 2 * 2 Example

This program allows the user to enter the rows and columns elements of a 2 * 2 Matrix. Next, we are going to find the determinant of this matrix.

/* C Program to find Determinant of a Matrix  - 2 * 2 */
 
#include<stdio.h>
 
int main()
{
 	int rows, columns, a[2][2], Determinant = 0;
  
 	printf("\n Please Enter the 2 * 2 Matrix Elements \n ");
 	for(rows = 0; rows < 2; rows++)
  	{
   		for(columns = 0;columns < 2; columns++)
    	{
      		scanf("%d", &a[rows][columns]);
    	}
  	}
     
	Determinant = (a[0][0] * a[1][1]) - (a[0][1] * a[1][0]);
  	
  	printf("\n The Determinant of 2 * 2 Matrix = %d", Determinant);
 	return 0;
}

OUTPUT

C Program to find Determinant of a Matrix 2

ANALYSIS

In this Program, we used for loop to iterate each and every cell present in a[2][2] matrix. Conditions inside the for loops ((rows < i) and (columns < j)) will ensure the compiler, not to exceed the matrix limit. Otherwise the matrix will overflow

scanf statement inside the for loop will store the user entered values in every individual array element such as a[0][0], a[0][1], …..

for(rows = 0; rows < i; rows++).
{
  for(columns = 0; columns < j; columns++)
   {
     scanf("%d", &a[rows][columns]);
   }
}

In the next line, We are calculating the Determinant

Determinant = (a[0][0] * a[1][1]) - (a[0][1] * a[1][0]);

User entered array a[2][2] = {{10, 20}, {30, 40}}

Determinant = (a[0][0] * a[1][1]) – (a[0][1] * a[1][0])

Determinant = (10 * 40) – (20 * 30)

Determinant = (400) – (600) = -200

C Program to find Determinant of a Matrix – 3 * 3 Example

This program is similar to above example but this time we are finding the determinant of 3 * 3 matrix.

/* C Program to find Determinant of a Matrix  - 3 * 3 */
 
#include<stdio.h>
 
int main()
{
 	int rows, columns, a[3][3];
	int x, y, z, Determinant = 0;
  
 	printf("\n Please Enter the 3 * 3 Matrix Elements \n");
 	for(rows = 0; rows < 3; rows++)
  	{
   		for(columns = 0;columns < 3; columns++)
    	{
      		scanf("%d", &a[rows][columns]);
    	}
  	}
  	
    x = (a[1][1] * a[2][2]) - (a[2][1] * a[1][2]);
    y = (a[1][0] * a[2][2]) - (a[2][0] * a[1][2]);
    z = (a[1][0] * a[2][1]) - (a[2][0] * a[1][1]);
	
	Determinant = (a[0][0] * x) - (a[0][1] * y) + (a[0][2] * z);
  	
  	printf("\n The Determinant of 3 * 3 Matrix = %d", Determinant);
 	return 0;
}

OUTPUT

C Program to find Determinant of a Matrix 3

ANALYSIS

In this C Program to find Determinant of a Matrix example, User entered array a[3][3] = {{10, 20, 30}, {40, 50, 60}, {70, 80, 90}}

x = (a[1][1] * a[2][2]) – (a[2][1] * a[1][2])

x = (50 * 90) – (80 * 60)

x = 4500  – 4800

x = -300

y = (a[1][0] * a[2][2]) – (a[2][0] * a[1][2])

y = (40 * 90) – (70 * 60)

y = 3600 – 4200

y = -600

z = (a[1][0] * a[2][1]) – (a[2][0] * a[1][1])

z = (40 * 80) – (70 * 50)

z = (3200) – (3500)

z = -300

Determinant = (a[0][0] * x) – (a[0][1] * y) + (a[0][2] * z)

Determinant = (10 * -300) – (20 * -600) + (30 * -300)

Determinant = (-3000) – (-12000) + (-9000)

Determinant = -3000 + 12000 – 9000 = 0