$(10$ points$)$ Consider matrix multiplication $C=AB,$ where $A$ is a $46$

matrix, $B$ is a $64$ matrix and $C$ is a $44$ matrix. Please describe this

operation in $\frac{C}{C}++$ language, where the element in the $i-$th row and the $j-$the

column of matrix $A$ is represented by $A[i][j]$ and so on$.$ Next, please do

tiling with $23$ tiles from A and $32$ tiles from $B.$ Please write

corresponding $\frac{C}{C}++$ code for this tiling. Assume there is only one level

cache, with size accommodating only $12$ elements and each access to

DRAM can only read$/$write one element. The cache replacement policy is

LRU $($least recently used$)$ except that partial$/$complete computing result is

always directly written into DRAM without storing in cache. Please estimate

the numbers of DRAM accesses without and with the tiling. For the $\frac{C}{C}++$

code, subroutine is not allowed, please focus on the kernel part and no need

to provide code for data IO$.$ For example, the inner product between two

vectors $U$ and $V$ with $N$ elements can be written in $C$ as

Please solve it by hand. Thanks.