Using fixed$-$size speedup and scalability analysis techniques, answer the following. $($a$)$ Analyze the running time of the serial algorithm as a function of the

matrix dimension n and m$.$ You may assume all operations take unit

time. $($More appropriate runtime order techniques will be presented

later in the course $$big O$$ notation.$)($b$)$ Analyze the running time of the parallel algorithm as a function of n$,$

m and p$.$ You may also assume n and m are evenly divisible by p$.($c$)$ Obtain expression for the speedup, S p$,$ and the Amdahl$$s fraction a$.($d$)$ Determine if the algorithm is effective. Briefly explain.