$($a$)$ Write a loop$-$based code that computes $$q$2,$ where q is size $1001.$ To test

your code and show that it works, use the rand function to create a vector q

with random entries. Store the value of $$q$2$ as a variable N$2$q$.$ Then, apply your

method. At the end of the loop, check your error with the following code:

looperror $=$ abs$($ norm$($q$,2)-$ N$2$q$)$

$($b$)$ Now write a code for computing $$q$2$ that avoids using any loops and instead uses

transposes and a matrix$-$vector product. Store your value in the variable N$2$qIP,

and then compute the error

IPerror $=$ abs$($ norm$($q$,2)-$ N$2$qIP$)$