solve (c) please!

5. Matrix Multiplication. (15 points) Recall that we used the divide-and-conquer paradigm to multiply matrices by partitioning the n x 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-conquer algorithm where instead of dividing the matrices into four n 2 n/2 sub-matrices, you would instead divide the x n/3 sub-matrices and you managed to have k sub-problems ltiplications of smaller sub-matrices). Write down the recurrence matrices into nine n/ as a res ult (i.e. k mul in terms of n and k Ho a subproblems k should we have (at most) in order for your re- (a) to pertorm better than Strassen's algorithm? Justify square matrices of size n x n ose you want to multiply two square matrices that are of pon n is a power of 2. t a power of 2. Explain how you can modify the algorithm des igned algorithm in part your answer by showing all your work (c) size m m where m is not a power of 2 or the matrices) so that Strassen's algorith