PART I: Do this in MATLAB

Create a vector $x$ containing all integers from $1$ to $100.$ Create a vector $Y$ containing the

following, in this order: $1,0\mathrm{.}9,0\mathrm{.}8,0\mathrm{.}7$dots$0\mathrm{.}1,0.$

Create a vector $U$ containing the first $25$ elements of $x.$ Create a vector $V$ containing elements

$50$ through $75$ of $x.$ Create a vector $W$ containing all the elements of $x$ with an even index.

Create a $33$ matrix with all ones. Create a $81$ matrix with all zeros. Create a $52$ matrix

with all elements equal to $0\mathrm{.}37.$

Create a $125$ vector containing random elements distributed in the interval $-0\mathrm{.}5,0\mathrm{.}5.$

Given matrix $M=[1,2,3$;$2,1,5$;$4,6,4$;$2,3,2],$ create another matrix $N$ containing first two

rows and the first and the third column $($i$.$e$.,$ row indexes $i=1,2$ and column indexes $j=1,3)$

from $M.$

Given vector $A=[8,6,4]$ and integer number $n=4$ create matrix $B$ containing n$-$times $A(1)$

in the first row, n$-$times $A(2)$ in the second row, etc. $($i$.$e$.$

$B=,[8,8,8,8$

$6,6,6,6$

$4,4,4,4]$

NOTE: You get full credit for this problem by attempting a solution. Just try it$.$

PART II: The sphere pictured to the right floats above

the surface of the water at a height that is proportional to

the mass of the person inside plus the mass of the sphere

material. The height, $h,$ is related to the mass, $m,$ by the

following equation:

$m=\frac{{}_w}{3}(4r^3+h^3-3r{h}^2)$

where ${}_w$ is the density of water, $1000k\frac{g}{m^3},$ and $r$ is

the radius of the sphere, $2$ m $.$ The mass of the empty

sphere material is $12$ kg $.$

A battery of tests were run before bringing this fun

device to market, including measuring the height of the

sphere above water while people of different weights

were inside. Download the height data from the Moodle

page. It is contained in a file called HW$2\_$data.txt$.$

Using the "load" command, bring the h values into a matrix, and use the "size" command to

find out how many data values are present.

In a second matrix use the equation above to find the mass of each participant in the test.

Remember to subtract the mass of the empty sphere.

What is the mass of participant $14?$ And participant $24?$

Find the average of the masses of participants $4,12,22,$ and $37.$