Homework Assignment #$2-$ Part $1$

This assignment is worth $100$ points and consists of two parts. This is Part $1,$ which covers matrix

manipulation and program flow control. Part $2$ will cover user$-$controlled data input and output. Both Part

$1$ and $2$ are due Tuesday, October $8^{th}$ on Canvas. Code must be written in MATLAB, be well

documented, and submitted as one $M$ file using sections.

The sum of the following geometric series converges to $2$ :

$1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+$cdots$=2$

Geometric series is a series of numbers in which the ratio of the next term to the previous one is the same.

In the above case it is $\frac{1}{2}.$ Write a script according to the following instructions:

a$)$ Using a while loop to check for convergence to $2.$ The convergence criterion is that difference

between the running total and the convergence value of $2$ should be equal to or less than the error

$0\mathrm{.}000001.$ The script should output the number of terms needed and the final sum.

b$)$ Repeat part $($a$)$ but use a for loop.

NOTE: Remember that in a while loop the conditional check is at the beginning of the loop and in a for

loop, if a conditional check is needed, it is OK to perform conditional check at the end of the loop, but

use the break command.

Consider the following matrices:

$A=\left[\begin{array}{cccc}2& 4& 6& 8\end{array}\right],B=\left[\begin{array}{c}5\\ 7\\ 9\\ 11\end{array}\right]$

Perform the following operations.

a$)$ Create two new matrices U and V respectively using meshgrid function using A and B as input row

vectors.

b$)$ Create a new matrix Z by dot multiplying U with V $.$

c$)$ Create a matrix $x$ which is similar to $U$ but this time use the repmat function. Repeat this problem,

but create a matrix Y similar to V using the repmat function.

d$)$ Create a matrix Q by dot dividing Z with X $.$Homework Assignment #$2-$ Part $2$

This assignment is worth $100$ points and consists of two parts. This is Part $2,$ which covers user$-$controlled

data input and output. Both Part $1$ and $2$ are due Tuesday, October $8^{th}$ on Canvas. Code must be

written in MATLAB, be well documented, and submitted as one M file using sections.

Recall the convergent geometric series from Problem #$1$ of Homework #$2$ Part #$1.$ For this problem,

write a script that performs the following:

Prompt the user for input in the form of the number of terms to compute. Check for valid input,

and loop until the user enters a positive number greater than zero. If an invalid number is entered,

display a message reminding the user to enter a positive integer.

Use fprintf to output to the command window each term. See below for an example of what I

would like for the formatted output. Also, output to the command window the total as well as the

number of terms, as shown below. You may use either a while loop or for loop.

Example of the user entering $5($five terms$)$:$1\mathrm{.}00000+0\mathrm{.}50000+0\mathrm{.}25000+0\mathrm{.}12500+0\mathrm{.}06250=1\mathrm{.}93750,"$ number of terms $"=5$

Specify five decimal places to the right of the decimal point for each term and the total, and no decimal

places for the number of terms.