Recall that if $A$ is an $mn$ matrix and $B$ is a $pq$ matrix, then the product $C=AB$ is defined if and only if $n=p,$ in which case $C$ is an $mq$ matrix.

Each row of the matrix $AB$ can be computed as the product of the corresponding row of A times the matrix $B$ :

$AB=\left[\begin{array}{c}\text{v}\text{e}\text{c}(a{)}_{1}B\\ \text{v}\text{e}\text{c}(a{)}_{2}B\\ \text{v}\text{d}\text{o}\text{t}\text{s}\\ \text{v}\text{e}\text{c}(a{)}_{m}B\end{array}\right]$

$.$vec$(c{)}_i=$vec$(a{)}_{i}B,$ where vec$(c{)}_i$ and vec$(a{)}_i$ are the th rows of $C$ and A respectively.

For instance, if $A$ is $34$ and $B$ is $45,$ the product $AB$ is given by the matrix:

$C=\{A(1,$:$)**B$;$A(2,$:$)**B$;$A(3,$:$)**B\}$

Write a function named rowproduct that takes as input two matrices A and $B$ and a random number $k,$ and as output produces the product, $C,$ by rows of the two matrices and the intermediate value, $z,$ of the output matrix at the end of $k$ iterations $($the matrix $z$ is used by MATLAB Grader to determine whether your code is correct$).$

The function should work for any dimension of A and $B$ and it should perform a check to see if the dimensions match and return an empty product matrix if the dimensions do not match.

Specific instructions for writing the function:

Extract the dimension of A using the command size and store the result in the variables $m$ and $n.$

Extract the dimension of $B$ using the command size and store the result in the variables $p$ and $q$

Use an if statement to perform a check on the dimensions to determine whether the multiplication is defined

If the multiplication is defined:

initialize $C$ as a matrix of zeros of the appropriate dimension

use a single for loop to evaluate the product $C=AB.$ The loop counter should be the variable $i.$ Each iteration of the for loop should evaluate the ith row of the matrix $C$ as the product of the $i$ th row of the matrix A times the matrix B$.$ Also, inside the for loop, after you compute the ith row of C$,$ insert the following commands:

if isequal $(i,k)$