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Determinant of a Matrix in C++ Program
In this tutorial, we are going to learn how to find the determinant of a matrix.
Let's see the steps to find the determinant of a matrix.
Initialize the matrix.
Write a function to find the determinant of the matrix.
If the size of the matrix is 1 or 2, then find the determinant of the matrix. It's a straightforward thing.
Initialize variables for determinant, submatrix, sign.
Iterate from 1 to the size of the matrix N.
Find the submatrix for the current matrix element.
All the elements that are not in the current element row and column
Add the product of the current element and its cofactor to the determinant.
Alter the sign.
Print the determinant of the matrix.
Example
Let's see the code.
#include <bits/stdc++.h>
using namespace std;
#define N 3
void subMatrix(int mat[N][N], int temp[N][N], int p, int q, int n) {
int i = 0, j = 0;
// filling the sub matrix
for (int row = 0; row < n; row++) {
for (int col = 0; col < n; col++) {
// skipping if the current row or column is not equal to the current
// element row and column
if (row != p && col != q) {
temp[i][j++] = mat[row][col];
if (j == n - 1) {
j = 0;
i++;
}
}
}
}
}
int determinantOfMatrix(int matrix[N][N], int n) {
int determinant = 0;
if (n == 1) {
return matrix[0][0];
}
if (n == 2) {
return (matrix[0][0] * matrix[1][1]) - (matrix[0][1] * matrix[1][0]);
}
int temp[N][N], sign = 1;
for (int i = 0; i < n; i++) {
subMatrix(matrix, temp, 0, i, n);
determinant += sign * matrix[0][i] * determinantOfMatrix(temp, n - 1);
sign = -sign;
}
return determinant;
}
int main() {
int mat[N][N] = {{2, 1, 3}, {6, 5, 7}, {4, 9, 8}};
cout << "Determinant: " << determinantOfMatrix(mat, N) << endl;
return 0;
}Output
If you execute the above program, then you will get the following result.
Determinant: 36
Conclusion
If you have any queries in the tutorial, mention them in the comment section.
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