84 lines
2.7 KiB
Java
84 lines
2.7 KiB
Java
|
/*
|
||
|
|
This is the java program to check whether the matrix is invertible or not. The square matrix is invertible if and only if its determinant is non zero.
|
||
|
|
*/
|
||
|
|
|
||
|
|
//This is a simple program to check whether the matrix is invertible or not.
|
||
|
|
//The complexity of the algorithm is O(n^3)
|
||
|
|
|
||
|
|
import java.util.*;
|
||
|
|
|
||
|
|
public class Invertible_Matrix
|
||
|
|
{
|
||
|
|
public 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 input = new Scanner(System.in);
|
||
|
|
System.out.println("Enter the order of the square matrix");
|
||
|
|
int n = input.nextInt();
|
||
|
|
System.out.println("Enter the elements of the square matrix");
|
||
|
|
double[][] mat = new double[n][n];
|
||
|
|
for(int i=0; i<n; i++)
|
||
|
|
{
|
||
|
|
for(int j=0; j<n; j++)
|
||
|
|
{
|
||
|
|
mat[i][j] = input.nextDouble();
|
||
|
|
}
|
||
|
|
}
|
||
|
|
Invertible_Matrix I = new Invertible_Matrix();
|
||
|
|
if(I.determinant(mat, n) == 0)
|
||
|
|
{
|
||
|
|
System.out.println("Matrix is not Invertible, as the determinant is : "+I.determinant(mat, n));
|
||
|
|
}
|
||
|
|
else
|
||
|
|
{
|
||
|
|
System.out.println("Matrix is Invertible, as the determinant is : "+I.determinant(mat, n));
|
||
|
|
}
|
||
|
|
input.close();
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
/*
|
||
|
|
Enter the order of the square matrix:
|
||
|
|
3
|
||
|
|
Enter the elements of the square matrix:
|
||
|
|
1 2 3
|
||
|
|
4 5 6
|
||
|
|
7 8 9
|
||
|
|
Matrix is not Invertible, as the determinant is : 0.0
|