Exercise $1.$ Sum of some entries $(20$ points$)$

Consider the outer product $x$:$={?}^{TT},n{R}^n,$ where $R^n$ denotes the set of all $n1$ vectors

with real entries. Without using any loops $($such as for, while, if else$),$ we want to write a

MATLAB function named SumOuterProduct.m that takes an arbitrary vector $xin{R}^n$ as

input and outputs the scalar $s,$ equal to the sum of all entries on or above the main diagonal

of the matrix $x.$

Write a MATLAB executable file YourlastnameYourfirstnameHW$2$p$1.$m for a random vec$-$

tor $n{R}^{100}$ to compute $s$ as follows.

close all; clear; clc

$x=$rand$(100,1)$;

$s=$ SumOuterProduct $(x)$;

The file YourlastnameYourfirstnameHW$2$p$1.$m should have exactly the above three lines and

nothing else. Please make sure to keep both the $.$m files in the same folder$/$directory so that

the executable file can "see" the function it calls. Submit both $.$m files.

Hint: For your MATLAB function file, use the command sum $($look it up in MATLAB

documentation$)$ and basic arithmetic operations such as addition $(+),$ multiplication ${(}^{**}),$

power $(hat(.)).$ You will not need any built$-$in commands other than these.