Program to check if matrix is singular or not

Last Updated : 06 Aug, 2024

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 functions int 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 functions if __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# 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

Program to check if matrix is singular or not

Manish_100

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Program to check if matrix is singular or not

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