Code:
#include conio.h
#include iostream
#include math.h
using namespace std;
double d = 0;
double det(int n, double mat[10][10]);
double det(int n, double mat[10][10])
{
double submat[10][10];
if (n == 2)
return ((mat[0][0] * mat[1][1]) - (mat[1][0] * mat[0][1]));
else
{
for (int c = 0; c < n; c++)
{
int subi = 0; //submatrix's i value
for (int i = 1; i < n; i++)
{
int subj = 0;
for (int j = 0; j < n; j++)
{
if (j == c)
continue;
submat[subi][subj] = mat[i][j];
subj++;
}
subi++;
}
d = d + (pow(-1, c) * mat[0][c] * det(n - 1, submat));
}
}
return d;
}
int main(int argc, char **argv)
{
cout << "Enter the number of vectors:\n";
int n;
cin >> n;
double mat[10][10];
cout << "Enter the vectors one by one:\n";
for (int i = 0; i < n; i++)
{
for (int j = 0; j < n; j++)
{
cin >> mat[j][i];
}
}
d = det(n, mat);
if (d != 0)
cout << "The vectors forms the basis of R" << n
<< " as the determinant is non-zero";
else
cout << "The vectors doesn't form the basis of R" << n
<< " as the determinant is zero";
}
Output:
Enter the number of vectors:
3
Enter the vectors one by one:
1 2 3
2 3 4
3 4 5
The vectors doesn't form the basis of R3 as the determinant is zero
Enter the number of vectors:
4
Enter the vectors one by one:
2 3 5 8
1 6 2 9
3 4 2 7
2 5 3 9
The vectors forms the basis of R4 as the determinant is non-zero
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