(Application of LU factorization): When computing the determinant of a matrix by hand, it is common to use cofactor expansion and apply the definition recursively. But this is terribly inefficient as a function of the matrix size. (a) (By Hand) Explain why, if A = LU is an LU factorization, where uii, li, i=1,2,.. TL det (A) = u1122l22 Unnlnn = [, i=1 ,n are the diagonal elements of U and L respectively. (b) (By Matlab)Using the result of part (a), write a MATLAB function determinant that computes the determinant of a given matrix A using mylu from lecture. Include the function at the end of your live script. Display the determinant of the matrices magic(n) for n = 3,4, ..., 7 by using your function built in (b) and the Matlab built-in function det.