C Code - Determinant (Recursion ONLY!)

Q14. Determinant [12 marks] In linear algebra, the determinant of a square matrix is a useful value that plays an important role in finding the inverse of a matrix, among other uses. The determinant of a square matrix A is denoted by det A, or |Al, and can be computed from the elements of the matrix. In the case of a 2 x 2 matrix A, the determinant is the product of the diagonal elements, subtracted by the product of the anti-diagonal elements, as shown below: ad-bc For a 3 x 3 matrix B, its determinant |B is as shown below: = a(ei-fh)-b(di-fg) + c(dh-eg) It looks complicated but there is a general pattern. To work out the determinant of a 3x 3 matrix, we compute the following 3 terms one by one The 1st term is the result of multiply a by the determinant of the 2 x 2 matrix that is not a's row or column (see below). This determinant of a smaller matrix is called a minor of the matrix. We do the same to compute the 2nd term (with b) and the 3rd term (with e) Note that the 2nd term has a negative sign. The determinant of the matrix is the sum of these 3 terms. The same procedure can be used to find the determinant of a 4 4 matrix (4 terms), a 5 x 5 matrix (5 terms), and so on. Note that the alternate terms (i.e., the 2nd, 4th, 6th, ..., terms) have a negative sign rite a recursive function int determinant (int mtx [] [10], int size) that computes the determinant of a square matrix. Your function should take in a square matrix mtx and the size of the matrix. It thern calculates and returns the determinant of mtx You may assume that size is an integer in [2, 10] No marks will be awarded if the function is NOT recursive (Hint 1: The base case is when the size of the matrix is 2.) (Hint 2: A minor of the matrix can be computed using the determinant function if the values of the smaller matrix are stored in a 2D array.) [12 marks]