Write a MATLAB function with inputs

$$ a matrix A of size m $\backslash$times n$,$

$$ a vector x of size n $\backslash$times $1,$

and which outputs the product vector Ax $($note that the size of this vector should be

m $\backslash$times $1).$

To get the dimensions of the matrix A$,$ you can use

$[$m$,$n$]=$ size$($A$)$;

similarly to how we got the length of the vector u as

n $=$ length$($u$)$;

Here the semicolon supresses output.

Your code should check that the sizes of the inputs are right and then do the multiplication using two nested $$for$$ loops.

a$)$ Run your code on A $=$ rand$(9)$ and x $=$ rand$(9,1)($the command $$rand$$ produces

a random matrix$).$ Compare the output of your function to the result when you

type A $$ x into MATLAB $($the results should be the same!$).$

b$)$ How many floating point operations $($additions and multiplications$)$ does the code

use? Find a formula in terms of m and n$.($Similar to how we found that a vectorvector multiplication takes $2$n $($or $2$n$1,$ depending on how you count$)$ operations,

where n is the vector length.$)$