$($a$)$ Why do we need parallel computing systems? State some important applications of parallel computers.

$($b$)$ Explain the different types of parallelism exploited by contemporary parallel computing systems.

$($c$)$ Explain the major$$s problems faced to achieve a linear speedup with parallel computers.

$($d$)$ Suppose you want to achieve a speed$-$up of $8$ times faster with $10$ processors. What percentage of the original computation can be sequential?

$($e$)$ Suppose we want to perform two sums: one is a sum of $10$ scalar variables, and one is a matrix sum of a pair of two$-$dimensional arrays, with dimensions $20$ by $20.$ Assume only the matrix sum is parallelizable. Show all your work to get full credit. $($i$)$ What speedup we get with $10$ processors assuming the load on each processor is balanced? $($ii$)$ What speedup we get with $10$ processors where one processor gets $20\%$ of the load?