The product $y=Ax$ of an $mn$ matrix A times a vector $x=(x_1,x_2,$dots,$x_n{)}^T$ can be

computed row$-$wise as

$y=[A(1,$:$)**x$;$A(2,$:$)**x$;dots;$A(m,$:$)**x]$;

that is

$y(1)=A(1,$:$)**x$

$y(2)=A(2,$:$)**x$

cdots

$y(m)=A(m,$:$)**x$

Write a function M$-$file that takes as input a matrix A and a vector $x,$ and as output gives

the product $y=Ax$ by row, as defined above $($Hint: use a for loop to define each entry of

the vector $y.)$

Your M$-$file should perform a check on the dimensions of the input variables A and $x$ and

return a message if the dimensions do not match. Call the file myrowproduct.m$.$

Note that this file will NOT be the same as the myproduct.m example.

Test your function on a random $25$ matrix A and a random $51$ vector $x.$ Compare the

output with $A**x.$

Repeat with a $54$ matrix and a $41$ vector and with a $54$ matrix and a $14$ vector.

Use the command rand to generate the random matrices for testing.

Include in your lab report the function M$-$file and the output obtained by running it$.$