Let M1, M2, . . . , Mn be a sequence of matrices. Each matrix Mi has dimension ri-1 ri, The minimum cost of multiplying matrices Mi x M2 x... x Mn can be computed as follows. Let cij, i Sj, be the minimum cost of multiplying matrices M x Mi+x... x Mj. Then we can show that if j i (a) (10) Design an efficient algorithm to compute these cij's in a way that when cij is to be computed, all the cik's and all the ck+ls which are needed have already been computed. (b) (5) Use n 8 as an example to show the order of the ci's are computed by your algorithm. (c) (5) Which cij is the minimum cost to multiply these matrices