/*

This is the java program to find whether the vectors entered by users form the basis for the given dimension.
The result for the same can be obtained by checking whether the determinant of the matrix formed by vectors is zero or not.
If the determinant is non zero its forms the basis for the given dimension, not otherwise.
*/

//This is a sample program to find the basis and dimension of a vectors
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<N; 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<N; i++)
                            {
                                int j2=0;
                                for(int j=0; j<N; 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<n; i++)
            {
                for(int j=0; j<n; 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();
    }
}

/*
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