Write a program that uses a recursive algorithm to calculate the determinant of a matrix. The matrix must be implemented with one or more linked lists. No memory should be allocated for zero valued matrix elements.The program should read a matrix and calculate and print the determinant. Your matrix implementation should be that of a "sparse" matrix. Only matrix elements that are non-zero should be allocated in memory. This means you cannot implement your matrix with a 2D array.

The input is a matrix of integers.

The output is the determinant of the matrix.

If the matrix is not square, an error message is given.

Sample Input 1:

1 -2 3 -2 3 -2 3 -1 2

Sample Output 1:

-13

Sample Input 2:

1 2 3 4 1 1 1 1 4 3 2 1 1 1 1 1

Sample Output 2:

0

Sample Input 3:

1 2 3 4 5 6

Sample Output 3:

Error! Non-square matrix!

Sample Input 4:

0 0 0 0

Sample Output 4:

0

Sample Input 5:

0 1 1 0

Sample Output 5:

-1

Sample Input 6:

1 0 2 -1 0 -1 0 1 0

Sample Output 6:

-1

Sample Input 7:

5 4 -3 2 1 -1 -3 3 -4 -5 1 1 5 1 10 -2 2 -2 2 -2 1 1 1 1 1

Sample Output 7:

-640

Sample Input 8:

1 2 3 3 4 5 5 6

Sample Output 8:

Error! Non-square matrix!

Recall that the formula for the determinant of a matrix is:

det=i=0numRows1((1)i+ja[i,j]det(Minor(a[i,j])))foranyjdet=i=0numRows1((1)i+ja[i,j]det(Minor(a[i,j])))foranyj

The minor of a matrix element x is the sub-matrix formed by removing the row and column containing x.

a= 0 4 1 3

1 3 2 4

2 3 1 9

1 8 2 1

and minor a(1, 2) removes row 1 and column 2

minor(a(1,2)) = 0 4 3

2 3 9

1 8 1

Can anyone help?

det 'urnRows- ( (-1)'+, . a li, j) . det (Minor (a [i, j)))) for any j