10. (a) Apply Strassen's algorithm to compute 4 4 Exiting the recursion when n = 2, i.e., computing the products of 2-by-2 matrices by the brute-force algorithm. How many multiplications would be performed in finding the product of two 64 *64 matrices using the standard algorithm? How many multiplication would be performed in finding the product of two 64 * 64 (b) (c) matrices using Strassen's method? 11. Given two polynomials which have the following: P(1)-2x3 +3x -5 and P(2)-2 x3-3 x2+1 (a) Use their coefficient representations and ordinary multiplication method to find the product P(1) and P(2) (b) Use Fast Fourier Transform (FFT) approach to finding the solution of their product 12. Rank (and show) the following functions by order of growth (use the limit as n goes to infinite to justify your claims) g(lg*n) 2lg'n (V2)e n (lg n)! lg(n!) ngn g* n (Ig n)le 2/2Ign In In n In n 4 2m+1 lg* (Ig n) nlg n