Question

Programming Language: Java Please write a program that uses a recursive algorithm to compute the determinant of a matrix. It should read the order of the matrix, read the matrix, print it out, compute, and print the determinant. Your program should be able to evaluate multiple matrices on a single execution. For class purposes, your program should handle matrices up to and including those of order 6. You are required to use an array for this problem. Your solution must be recursive.

Justify your data structures. Consider an iterative implementation. Would it be more efficient? What data structures would you choose in that case?

As a minimum, use the following eight matrices to test your program, formatted as

shown below, with the order of the matrix preceding it.

1 x 1: [5]

2 x 2: 2 3

5 9

3 x 3: 3 -2 4

-1 5 2

-3 6 4

4 x 4: 2 4 5 6

0 3 6 9

0 0 9 8

0 0 0 5

4 x 4: 2 4 5 6

0 0 0 0

0 0 9 8

0 0 0 5

6 x 6:

6 4 6 4 6 4

1 2 3 4 5 6

6 5 4 3 2 1

3 2 3 2 3 2

4 6 4 6 4 6

1 1 1 1 1 1

Answer 1

Hi,

Please find the below java code which determines the Determinant of a given matrix.

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MatrixDeterminantDemo.java

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import java.util.Scanner;

public class MatrixDeterminantDemo {

   // 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 for finding determinant of matrix. n is current dimension
   * of mat[][].
   */
   static int determinantOfMatrix(int mat[][], int n) {
       int D = 0; // Initialize result

       // Base case : if matrix contains single
       // element
       if (n == 1)
           return mat[0][0];

       // To store cofactors
       int temp[][] = new int[n][n];

       // To store sign multiplier
       int sign = 1;

       // 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] * determinantOfMatrix(temp, n - 1);

           // terms are to be added with
           // alternate sign
           sign = -sign;
       }

       return D;
   }

   /* function for displaying the matrix */
   static void display(int mat[][], int row, int col) {
       for (int i = 0; i < row; i++) {
           for (int j = 0; j < col; j++)
               System.out.print(mat[i][j]);

           System.out.print("\n");
       }
   }

   // Driver code
   public static void main(String[] args) {
       // initialize here.
       int row, col, i, j;
       Scanner scan = new Scanner(System.in);
       // enter the order of matrix
       System.out.print("Enter the order of matrix : ");
       row = scan.nextInt();
       col = row;
       int arr[][] = new int[row][col];
       // enter array elements.
       System.out.println("Enter " + (row * col) + " Array Elements : ");
       for (i = 0; i < row; i++) {
           for (j = 0; j < col; j++) {
               arr[i][j] = scan.nextInt();
           }
       }

       // the 2D array is here.
       System.out.print("The Array is :\n");
       for (i = 0; i < row; i++) {
           for (j = 0; j < col; j++) {
               System.out.print(arr[i][j] + " ");
           }
           System.out.println();
       }

       int mat[][] = { { 1, 0, 2, -1 }, { 3, 0, 0, 5 }, { 2, 1, 4, -3 }, { 1, 0, 5, 0 } };

       System.out.print("Determinant " + "of the matrix is : " + determinantOfMatrix(mat, row));
   }
}

Sample output 1:

Thanks!!