A matrix is said to be singular if the determinant of the matrix is 0 otherwise it is non-singular .
Examples:
Input : 0 0 0
4 5 6
1 2 3
Output : Yes
Determinant value of the matrix is
0 (Note first row is 0)
Input : 1 0 0
4 5 6
1 2 3
Output : No
Determinant value of the matrix is 3
(which is non-zero).First find the determinant of the matrix and the check the condition if the determinant id 0 or not, if it is 0 then matrix is a singular matrix otherwise it is a non-singular matrix .
Implementation:
C++
// C++ program check if a matrix is// singular or not.#include <bits/stdc++.h>using namespace std;
#define N 4// Function to get cofactor of mat[p][q] in temp[][].// n is current dimension of mat[][]void getCofactor(int mat[N][N], int temp[N][N], int p,
int q, int n)
{ int i = 0, j = 0;
// Looping for each element of the matrix
for (int row = 0; row < n; row++) {
for (int col = 0; col < n; col++) {
// Copying into temporary matrix only
// those element which are not in given
// row and column
if (row != p && col != q) {
temp[i][j++] = mat[row][col];
// Row is filled, so increase row
// index and reset col index
if (j == n - 1) {
j = 0;
i++;
}
}
}
}
}/* Recursive function to check if mat[][] is singular or not. */
bool isSingular(int mat[N][N], int n)
{ int D = 0; // Initialize result
// Base case : if matrix contains single element
if (n == 1)
return mat[0][0];
int temp[N][N]; // To store cofactors
int sign = 1; // To store sign multiplier
// Iterate for each element of first row
for (int f = 0; f < n; f++) {
// Getting Cofactor of mat[0][f]
getCofactor(mat, temp, 0, f, n);
D += sign * mat[0][f] * isSingular(temp, n - 1);
// terms are to be added with alternate sign
sign = -sign;
}
return D;
}// Driver program to test above functionsint main()
{ int mat[N][N] = { { 4, 10, 1 },
{ 0, 0, 0 },
{ 1, 4, -3 } };
if (isSingular(mat, N))
cout << "Matrix is Singular" << endl;
else
cout << "Matrix is non-singular" << endl;
return 0;
} |
Java
// Java program check if a matrix is // singular or not. class GFG
{ static final int N = 3;
// Function to get cofactor of mat[p][q] in temp[][].
// n is current dimension of mat[][]
static void getCofactor(int mat[][], int temp[][], int p,
int q, int n)
{
int i = 0, j = 0;
// Looping for each element of the matrix
for (int row = 0; row < n; row++)
{
for (int col = 0; col < n; col++)
{
// Copying into temporary matrix only
// those element which are not in given
// row and column
if (row != p && col != q)
{
temp[i][j++] = mat[row][col];
// Row is filled, so increase row
// index and reset col index
if (j == n - 1)
{
j = 0;
i++;
}
}
}
}
}
/* Recursive function to check if mat[][] is
singular or not. */
static int isSingular(int mat[][], int n)
{
int D = 0; // Initialize result
// Base case : if matrix contains single element
if (n == 1)
{
return mat[0][0];
}
int temp[][] = new int[N][N]; // To store cofactors
int sign = 1; // To store sign multiplier
// Iterate for each element of first row
for (int f = 0; f < n; f++)
{
// Getting Cofactor of mat[0][f]
getCofactor(mat, temp, 0, f, n);
D += sign * mat[0][f] * isSingular(temp, n - 1);
// terms are to be added with alternate sign
sign = -sign;
}
return D;
}
// Driver code
public static void main(String[] args)
{
int mat[][] = {{4, 10, 1},
{0, 0, 0},
{1, 4, -3}};
if (isSingular(mat, N) == 1)
{
System.out.println("Matrix is Singular");
}
else
{
System.out.println("Matrix is non-singular");
}
}
}/* This code contributed by PrinciRaj1992 */ |
Python3
# python 3 program check if a matrix is# singular or not.global N
N = 3
# Function to get cofactor of mat[p][q] in temp[][].# n is current dimension of mat[][]def getCofactor(mat,temp,p,q,n):
i = 0
j = 0
# Looping for each element of the matrix
for row in range(n):
for col in range(n):
# Copying into temporary matrix only
# those element which are not in given
# row and column
if (row != p and col != q):
temp[i][j] = mat[row][col]
j += 1
# Row is filled, so increase row
# index and reset col index
if (j == n - 1):
j = 0
i += 1
# Recursive function to check if mat[][] is# singular or not. */def isSingular(mat,n):
D = 0 # Initialize result
# Base case : if matrix contains single element
if (n == 1):
return mat[0][0]
temp = [[0 for i in range(N + 1)] for i in range(N + 1)]# To store cofactors
sign = 1 # To store sign multiplier
# Iterate for each element of first row
for f in range(n):
# Getting Cofactor of mat[0][f]
getCofactor(mat, temp, 0, f, n)
D += sign * mat[0][f] * isSingular(temp, n - 1)
# terms are to be added with alternate sign
sign = -sign
return D
# Driver program to test above functionsif __name__ == '__main__':
mat = [[4, 10, 1],[0, 0, 0],[1, 4, -3]]
if (isSingular(mat, N)):
print("Matrix is Singular")
else:
print("Matrix is non-singular")
# This code is contributed by# Surendra_Gangwar |
C#
// C# program check if a matrix is // singular or not.using System;
class GFG
{ static readonly int N = 3;
// Function to get cofactor of mat[p,q] in temp[,].
// n is current dimension of mat[,]
static void getCofactor(int [,]mat, int [,]temp, int p,
int q, int n)
{
int i = 0, j = 0;
// Looping for each element of the matrix
for (int row = 0; row < n; row++)
{
for (int col = 0; col < n; col++)
{
// Copying into temporary matrix only
// those element which are not in given
// row and column
if (row != p && col != q)
{
temp[i, j++] = mat[row, col];
// Row is filled, so increase row
// index and reset col index
if (j == n - 1)
{
j = 0;
i++;
}
}
}
}
}
/* Recursive function to check if mat[,] is
singular or not. */
static int isSingular(int [,]mat, int n)
{
int D = 0; // Initialize result
// Base case : if matrix contains single element
if (n == 1)
{
return mat[0, 0];
}
int [,]temp = new int[N, N]; // To store cofactors
int sign = 1; // To store sign multiplier
// Iterate for each element of first row
for (int f = 0; f < n; f++)
{
// Getting Cofactor of mat[0,f]
getCofactor(mat, temp, 0, f, n);
D += sign * mat[0, f] * isSingular(temp, n - 1);
// terms are to be added with alternate sign
sign = -sign;
}
return D;
}
// Driver code
public static void Main(String[] args)
{
int [,]mat = {{4, 10, 1},
{0, 0, 0},
{1, 4, -3}};
if (isSingular(mat, N) == 1)
{
Console.WriteLine("Matrix is Singular");
}
else
{
Console.WriteLine("Matrix is non-singular");
}
}
}// This code contributed by Rajput-Ji |
Javascript
<script> // Javascript program check if a matrix is // singular or not.var N = 3;
// Function to get cofactor of mat[p,q] in temp[,]. // n is current dimension of mat[,] function getCofactor(mat, temp, p, q, n)
{ var i = 0, j = 0;
// Looping for each element of the matrix
for (var row = 0; row < n; row++)
{
for (var col = 0; col < n; col++)
{
// Copying into temporary matrix only
// those element which are not in given
// row and column
if (row != p && col != q)
{
temp[i][j++] = mat[row][col];
// Row is filled, so increase row
// index and reset col index
if (j == n - 1)
{
j = 0;
i++;
}
}
}
}
}/* Recursive function to check if mat[,] is singular or not. */function isSingular(mat, n)
{ var D = 0; // Initialize result
// Base case : if matrix contains single element
if (n == 1)
{
return mat[0][0];
}
var temp = Array.from(Array(N), ()=>Array(N));// To store cofactors
var sign = 1; // To store sign multiplier
// Iterate for each element of first row
for(var f = 0; f < n; f++)
{
// Getting Cofactor of mat[0,f]
getCofactor(mat, temp, 0, f, n);
D += sign * mat[0][f] * isSingular(temp, n - 1);
// terms are to be added with alternate sign
sign = -sign;
}
return D;
}// Driver code var mat = [[4, 10, 1],
[0, 0, 0],
[1, 4, -3]];
if (isSingular(mat, N) == 1)
{ document.write("Matrix is Singular");
} else{ document.write("Matrix is non-singular");
}// This code is contributed by noob2000.</script> |
Output:
Matrix is non-singular
Time complexity: O(n3)
Auxiliary space: O(n2), for temp array to store co-factors