Code:
import java.util.Scanner;
public class Basis_Dimension_Matrix
{
public static double determinant(double A[][],int N)
{
double det=0;
if(N == 1)
{
det = A[0][0];
}
else if (N == 2)
{
det = A[0][0]*A[1][1] - A[1][0]*A[0][1];
}
else
{
det=0;
for(int j1=0;j1
{
double[][] m = new double[N-1][];
for(int k=0;k<(N-1);k++)
{
m[k] = new double[N-1];
}
for(int i=1;i
{
int j2=0;
for(int j=0;j
{
if(j == j1)
continue;
m[i-1][j2] = A[i][j];
j2++;
}
}
det += Math.pow(-1.0,1.0+j1+1.0)* A[0][j1] * determinant(m,N-1);
}
}
return det;
}
public static void main(String args[])
{
Scanner sc = new Scanner(System.in);
System.out.println("Enter the number of vectors:");
int n = sc.nextInt();
double [][]mat = new double[n][n];
System.out.println("Enter the vectors one by one:");
for(int i=0; i
{
for(int j=0; j
{
mat[j][i] = sc.nextDouble();
}
}
double det = determinant(mat, n);
if(det != 0)
System.out.println("The vectors froms the basis of R"+n+" as the determinant is non-zero");
else
System.out.println("The vectors doesn't form the basis of R"+n+" as the determinant is zero");
sc.close();
}
}
Output:
Enter the number of vectors:
2
Enter the vectors one by one:
1 1
-1 2
The vectors froms the basis of R2 as the determinant is non-zero
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