C++ Program to Find Basis and Dimension of a Matrix

This is a C++ program to find Basis and Dimension of a Matrix.

Algorithm

Begin
   Function determinant() :
   It calculates determinant of the matrix.
   /*
      Arguments:
      n = number of elements.
      matrix[10][10] = input matrix.
   */
   declare the submatrix submatrix[10][10].
   //Body of the function:
   if (n == 2)
      return ((matrix[0][0] * matrix[1][1]) - (matrix[1][0] * matrix[0][1]))
   else
      Make a for loop c = 0 to n-1
         Declare and initialize submati = 0, submatj.
         Make a For loop i = 1 to n-1
         initialize subj = 0
         Make a For loop i = 1 to n-1
            if (j == c)
               continue
            submatrix[submati][submatj] = matrix[i][j].
            Increment subj.
         increment submati.
      Compute d = d + (pow(-1, c) * matrix[0][c] * determinant(n- 1, submatrix)).
End

Example

#include<iostream>
#include<math.h>
using namespace std;
double d = 0;
double determinant(int n, double matrix[10][10]) {
   double submatrix[10][10];
   if (n == 2)
      return ((matrix[0][0] * matrix[1][1]) - (matrix[1][0] *
      matrix[0][1]));
   else {
      for (int c = 0; c < n; c++) {
         int submati = 0,submatj;
         for (int i = 1; i < n; i++) {
            int subj = 0;
            for (int j = 0; j < n; j++) {
               if (j == c)
                  continue;
               submatrix[submati][submatj] = matrix[i][j];
               subj++;
            }
            submati++;
         }
         d = d + (pow(-1, c) * matrix[0][c] * determinant(n -
         1, submatrix));
      }
   }
   return d;
}
int main(int argc, char **argv) {
   cout << "Enter the number of elements:\n";
   int n;
   cin >> n;
   double matrix[10][10];
   cout << "Enter elements one by one:\n";
   for (int i = 0; i < n; i++) {
      for (int j = 0; j < n; j++) {
         cin >> matrix[j][i];
      }
   }
   d = determinant(n, matrix); //call the function
   if (d != 0)
      cout << "The elements form the basis of R" << n << " as the determinant is non-zero";
   else
      cout << "The elements don't form the basis of R" << n << " as the determinant is zero";
}

Output - 1

Enter the number of elements:
3 Enter elements one by one:
7 6 1
2 3 4
5 8 9
The elements form the basis of R3 as the determinant is
non-zero

Output - 2

Enter the number of elements:
4 Enter the elements one by one:
7 6 1 4
2 3 5 4
9 8 2 3
2 1 3 0
The elements don't form the basis of R4 as the
determinant is zero