Please help me write this code using Matlab. I will make sure to upvote. Also, can you explain where to save the functions so that they work as intended upon typing lab$1$ into the command window. Thanks so much.

Lab $1$: Introduction to Matlab

Read sections $1-3$ of the Matlab tutorial document. To solve the problems below, you will have to

explore Matlab functionality using the Matlab "help" and you may have to browse through some of

the other tutorials listed in the Resources section. Create a script file called lab$1.$m$,$ which will hold

all the commands necessary to produce the plots and computations below. Use comments to label

part $2,$ part $3,$ etc. Do not forget to move the file to your home directory before you leave the lab.

Vectors

$($a$)$ Generate a row vector $x$ of length $25$ containing the integers $9,10,11,$dots$33.$

$($b$)$ Generate a row vector $y$ containing $25$ values, each of whom is a random real number in the

interval $5,8.$

$($c$)$ Produce a new vector $v$ equal to the sum of the two vectors above.

$($d$)$ Plot the vector $v$ in $2.c.$

$($e$)$ Compute the following:

i$.c=\frac{x}{y}($element$-$by$-$element division, for example $(3339)$ divided by $([1,3,3])$ is $([3,1,3]))$

ii$.d=v^4($each element raised to the fourth power$)$

iii. The dot product of $x$ and $y$

$($f$)$ Plot the odd$-$index elements of the vector $v,$ that is$,v(1),v(3),v(5),$dots,$v(25).$

$($g$)$ Plot the elements of the vector $v$ between $10$ and $18,$ that is $v(10),v(11),v(12),$dots,$v(18).$

$($h$)$ Plot the vectors in $2.$a and $2.$c on the same plot, using different colors.

$($i$)$ Plot all the plots in $2.$d$-2.$g on the same figure.

Hint: help dot, colon, rand, plot, hold, subplot.

Functions

$($a$)$ Write a Matlab function named myfun$1()$ that implements the following function:

The function takes a scalar as the input and outputs a scalar $($no vectors involved$).$

$($b$)$ Plot the function myfun$11)$ between $x=-5$ and $x=5.$

$($c$)$ Write a Matlab function myfun$2()$ that takes an input vector of size greater than two and

computes the sum of all the values in the vector that are not prime numbers. $($Example: for the

vector $2,-8,3,12,$ the sum is $4).$ Apply your function to a vector of length $10$ of your choice

and also to the vector $x$ from question $2($a$).$

$($d$)$ Write a function myfun$3()$ that accepts as input arguments a vector $x$ and two scalars $m$ and $s$

and plots the function

$g(x)=\frac{1}{s\sqrt[\phantom{2}]{4}}$exp$(-\frac{1}{8}(\frac{x-m}{s}{)}^2)$

$($e$)$ Using the above function, plot $g(x)$ for a vector $x$ with values from $0$ to $5,$ step $0\mathrm{.}05,m=3\mathrm{.}6$

and $s=0\mathrm{.}56$

Hint: help function, abs$,$ if$,$ fplot, find, isprime, sum.

Complex numbers, Loops

$($a$)$ Create a vector of length $10$ filled with $10$ complex numbers of your choice. Among the values

there should be some purely real and some purely imaginary numbers.

$($b$)$ Plot the vectors containing the real parts, imaginary parts, magnitudes, and phases of the $10$

complex numbers. Plot them on four different plots on the same figure.

$($c$)$ Write a Matlab function myfun$4()$ that takes an input vector and goes through all its compo$-$

nents, one by one, printing out just the purely imaginary values. Apply your function to the

vector in $4.a$