Problem $4$: You experiment with a GPU to compute the following multiplication $C=AB,$ the elements of $A,B,$ and $C$ are all with the same bit$-$width. Please answer the following questions $($please show detailed steps.$)(20$ pts $+$ Bonus $10$ pts$).$

$A=\left[\begin{array}{ccc}{x}_{1,1}& \text{c}\text{d}\text{o}\text{t}\text{s}& x_{1,l}\\ \text{v}\text{d}\text{o}\text{t}\text{s}& \text{d}\text{d}\text{o}\text{t}\text{s}& \text{v}\text{d}\text{o}\text{t}\text{s}\\ x_{m,1}& \text{c}\text{d}\text{o}\text{t}\text{s}& x_{m,l}\end{array}\right]$ and $B=\left[\begin{array}{ccc}{y}_{1,1}& \text{c}\text{d}\text{o}\text{t}\text{s}& y_{1,n}\\ \text{v}\text{d}\text{o}\text{t}\text{s}& \text{d}\text{d}\text{o}\text{t}\text{s}& \text{v}\text{d}\text{o}\text{t}\text{s}\\ y_{l,1}& \text{c}\text{d}\text{o}\text{t}\text{s}& y_{l,n}\end{array}\right]$

a$)$ If one thread is used to computer one element in matrix $C,$ what types of Arithmetic Logic Unit $($ALU$)$ operators will be used to support the thread operation? $(5$ pts$)$

b$)$ For a single$-$thread operation. Please point out the number of operations for each type of ALU operation. $(5$ pts$)$

c$)$ If we compute on a SISD computer, what is the total number of operations required for each type of ALU operation to compute the entire matrix C$?(10$ pts$)$

d$)$ Based on the observation from the answer above, when executing on GPU, assuming we have sufficient hardware resources, please write a pseudocode for computing matrix $C.$ The code should clearly demonstrate the data movement and proper configuration of kernels and threading to optimize the parallelism. $($Bonus $10$ pts$)$