a$)$ Use the LogP model to design the optimal summation tree for T$=28,$ L$=5,$ g$=4,$ and o$=2.$ Attribute the number of values stored locally in the memory of each processor. Compare the single processor and parallel solutions.

b$)$Suggest MPI code that computes in parallel the sum of rows of a n$$n real matrix using p parallel processes, producing an n$-$element vector. In the beginning, the matrix is stored in the memory of one process, the root. Then, it is partitioned equally into p horizontal slices, which are then scattered between the p processes, so that each process receives a slice. Then, all processes compute the sum of rows of their slices in parallel, each producing an n$-$element vector. Finally, these n$-$element vectors are reduced so that the host will hold the resulting vector. Assume that p divides n$.$ Explain how the code works.