5. Suppose that we modify Strassen's algorithm by dividing each matrix A and B into 9 sub-matrices, each of size n/3n/3, and expressing the product of A and B using p multiplications of these sub-matrices. What is the minimum p for which the running time of this algorithm would be better than O(n3) ? What is the minimum p for which the running time of this algorithm would be better than O(nlog7) ? 6. Suppose that we modify the linear-time selection algorithm as follows: we divide the sequences into 7-tuples, take M to be the set of medians of these 7-tuples, and use the median of M as the splitter. Give the recurrence equation for this algorithm and explain what the running time will be