We know from class that computing the determinant of an nx nmatrix using LU decomposition has computational cost W (n. But how expensive is it to compute a determinant using the common recursive definition formula for determinants? (a) Determine the number of floating point operations required for calculating the determinant of an n n matrix using a straightforward implementation of the recursive definition of the determinant. (You can combine additions and multipli cations Hint: consider the number of flops done on each recursive level separately. How f Mathematical Sciences Monash U many determinants are to be computed on each recursive level? On each recursive level, how many flops does it take to compute each of these determinants? (By us- ing determinants that are one size smaller, computed on the next recursive level.) Then sum up over all the levels (give the result as a sum like 1".) (b) Find an approximation for the expression derived that is valid for large n. (Hint ould be a very simple expression, proporti this approximate result sh you wl need exp /2!3/3!+z'/4! +...) ional to n