5. Matrix Multiplication. (15 points) Recall that we used the divide-and-conquer paradigm to multiply matrices by partitioning the n n matrices into four (n/2) (n/2) sub-matrices then recursively multiplying these smaller sub-matrices. The resulting algorithm yielded a e(n) running time. (a) (4 points) Suppose that you redesigned the divide-and-conqu of dividing the matri matrices in as a result (i.e. k mult in terms of n and k er algorithm where instead ces into four n/2x n/2 sub-matrices, you would instead divide the x n/3 sub-matrices and you managed to have k sub-problems iplications of smaller sub-matrices). Write down the recurrence to nine n/ blems k should we have (at most) in order for your re- thm in part (a) to perform better than Strassen's algorithm? Justify (b) (7 points) How many subpro esigned algorit your answer by showing all your work. (4 points) Strassen's algorithm was shown to work on (c) square matrices of size n x n ose you want to multiply two square matrices that are of n is a power ower of 2. Explain how you can modify the algorithm size m x m where m is not a 2 or the matrices) so that Strassen's algorith