Determinant calculation of a square matrix is widely used in solving many applied Mathematics problems. Some of them are while solving a set of linear equations using Cramer's rule (iff they have unique solutions), calculation of inverse matrix, Eigen values/ Eigen vectors problem and so on.

The determinant of a square matrix A∈R

det(A) = SUM

.

The summation is over all n! permutations(ν1,ν2,...,νn) of the integers 1,2,...,n, and sign(ν1,ν2,...,νn) = +1 or−1 depending on whether the n-tuple (ν1,ν2,...,νn) is an even or odd permutation of (1,2,...,n), respectively. An even (odd) permutation is obtained by an even (odd) number of exchanges of two adjacent elements in the array(1,2,...,n). A matrix A∈R

det(A) is nonzero.

Here, we've presented the determinant calculator of a square matrix in C:

Sample Output:

Enjoy coding !!!

The determinant of a square matrix A∈R

^{n×n}is the real number det(A) defined as follows:det(A) = SUM

_{perm }[sign(ν1,ν2,...,νn)a1ν1a2ν2...anνn].

The summation is over all n! permutations(ν1,ν2,...,νn) of the integers 1,2,...,n, and sign(ν1,ν2,...,νn) = +1 or−1 depending on whether the n-tuple (ν1,ν2,...,νn) is an even or odd permutation of (1,2,...,n), respectively. An even (odd) permutation is obtained by an even (odd) number of exchanges of two adjacent elements in the array(1,2,...,n). A matrix A∈R

^{n×n}is said to be non-singular when its determinantdet(A) is nonzero.

Here, we've presented the determinant calculator of a square matrix in C:

```
#include<stdio.h>
void readmatrix(int m[][8], int s){
int i,j;
printf("Enter elements of the matrix: \n");
for(i=0;i<s;i++)
for(j=0;j<s;j++)
scanf("%d", &m[i][j]);
}
int determinant(int m[][8],int s){
int i, j, k, det,cramermatrix[15][15], product, plussum = 0, minussum = 0;
if (s == 2)
det = m[0][0]*m[1][1] - m[0][1]*m[1][0];
else
{
for(i=0;i<s;i++)
for(j=0;j<s;j++)
cramermatrix[i][j] = m[i][j];
for(i=0;i<s;i++)
for(j=s;j<(2*s-1);j++)
cramermatrix[i][j] = m[i][j-s];
for(i=0;i<s;i++){
product = 1;
for(j = 0; j <s; j++)
product = product*cramermatrix[j][i+j];
plussum += product;
}
for(i=s-1;i<(2*s-1);i++){
product = 1;
for(j = 0; j <s; j++)
product = product*cramermatrix[j][i-j];
minussum += product;
}
det = plussum - minussum;
}
return det;
}
int main(){
int matrix[8][8], det, size;
printf("Enter the order of square matrix (n*n) e.g. 4 : ");
scanf("%d", &size);
readmatrix(matrix, size);
det = determinant(matrix, size);
printf("\n The determinant of the given square matrix is\n det = %d\n\n", det);
return 0;
}
```

Sample Output:

```
Enter the order of square matrix (n*n) e.g. 4: 3
Enter the elements of the matrix:
3 4 5
0 1 1
0 1 -1
Determinant of the given matrix is
det = -6
```

Enjoy coding !!!

For more news, please head over to our website，mmopixel has an awesome offer for you. You can purchase GW2 Gold price or GW2 Legendary Weapons from us whenever you need any of them.

ReplyDeleteSEGA GENESIS - GAN-GAMING

ReplyDeleteSEGA GENESIS. septcasino GENESIS-HANDS. https://sol.edu.kg/ Genesis (JP-EU). NA. NA. gri-go.com NA. SEGA GENESIS-HANDS. NA. SEGA GENESIS. NA. GENESIS-HANDS. https://tricktactoe.com/ NA. worrione

After that, want to|you should|you have to} deposit any handy and obtainable on your cryptocurrency within the "Deposit" section. Then have the ability to|you probably can} just go to the page of any of the introduced online slots and begin spinning reels. Among the introduced gaming machines, each user can choose one thing for themselves and begin their means within the area of gambling. There are both traditional online slots with easy controls and clear combos and multi-purpose gambling machines with lots of bonus rounds and perks. 9 Masks of 제왕카지노 Fire is a hard and fast|a set} jackpot that offers the opportunity to win up to as} $2,000.

ReplyDelete