Consider the matrix $*$ vector product problem $(A^{**}x=y).$ The following shows pseudo code

for sequential version

Assume the matrix $A$ is distributed using row striping and $\frac{n}{p}$ rows distributed to

each processor. Likewise, $\frac{n}{p}$ elements of the vector are distributed to each of the $p$

processors.

When using MPI, we need to scatter A and $x$ to $p$ processors. To complete computation,

we need to perform all$-$to$-$all broadcast where each processor broadcasts its $\frac{n}{p}$ elements

of $x$ to other processors. Finally, we need to perform a gather operation to collect the result

vector y elements.

a$).$ Write an outline of the MPI code to perform the above matrix $*$ vector product. You don't

have to be exact with the syntax but show what MPI features you would use.

b$).$ Assuming that you have a ring network, compute the execution time of the algorithm

that includes both communication and computation costs.