1.1 Chapter

1)Assume we add a new protocol to the application layer. What changes do we need to make to other layers?

2) During the weekend, Professor xyz often needs to access files stored on his office desktop from his home laptop. Last week, he installed a copy of the FTP server process on his desktop at his office and a copy of the FTP client process on his laptop at home. He was disappointed when he could not access his files during the weekend. What could have gone wrong?

3) Most of the operating systems installed on personal computers come with several client processes, but normally no server processes. Explain the reason.

4) Assume a TELNET client uses ASCII to represent characters, but the TELNET server uses EBCDIC to represent characters. How can the client log into the server when character representations are different?

5) Can you find an analogy in our daily life as to when we use two separate connections in communication similar to the control and data connections in FTP?

3.2 Chapter

1)List four types of delays in a packet-switch network.

2) Describe the three auxiliary protocols at the network layer of the TCP/IP suite that are designed to help the IPv4 protocol.

3) Describe the difference between multicasting and multiple-unicasting.

4) Explain why we can have different intradomain routing protocols in different ASs, but we need only one interdomain routing protocol in the whole internet.

4.1 Chapter

1) How does a single bit error differ from a burst error?

2) Explain why collision is an issue in random access protocols but not in controlled access or channelizing protocols.

3) How does a VLAN save a company time and money?

4) How does a VLAN reduce network traffic?

5) Discuss the functions of each SONET layer.

5.1 Chapter

1)Explain why the MAC protocol is more important in wireless LANs than in wired LANs.

2) What is multipath propagation? What is its effect on wireless networks?

3) An AP may connect a wireless network to a wired network. Does the AP need to have two MAC addresses in this case? Why or why not?

4) An AP in a wireless network plays the same role as a link-layer switch in a wired network. However, a link-layer switch has no MAC address, but an AP normally needs a MAC address. Explain the reason.

6.1 Chapter

1) We send a voice signal from a microphone to a recorder. Is this baseband or broadband transmission?

2) Describe PCM.

3) Which of the three multiplexing techniques are used to combine analog signals?

4) Name the two major categories of transmission media.

5) What are the three major classes of guided media?

6) What is the purpose of cladding in an optical fiber?

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MATH 240 – SPRING 2016

What to turn in: For this project you will need to turn in a printout of your published m-file.

Use a YourName_MATH240_Proj2.m file to save your code in an .m file. Use the command

PUBLISH(FILE,FORMAT) (or similar) to publish your work in word or pdf format (while you

are at it, play to see what other formats you can get). Make sure that you have enough comments

and results shown so that another person (me or the TA) can understand what you are doing).

Use %% notation to differentiate in cells the problems in this homework. This way you can even

run/debug one problem at a time.

Please apply the instructions from Project 1 about working in teams and labeling your project.

Remember to use the command lookfor *&% when trying to find the MATLAB command whose

description contains *&%.

MATLAB PROJECT 2:

The goals of this project are: (1) to learn more about how to quickly generate matrices using

MATLAB functions; (2) practice different ways of computing the inverse and use the properties

of determinants; (3) practice your understanding of the standard matrix of a linear

transformation; (4) interpret and explain the results generated by MATLAB.

PROBLEM 1: Use MATLAB commands to efficiently (i.e. without keying each entry) enter the

matrix:𝑆 =

[ 0 0 7 0 2 0 0 0 3 0 0 0 0

0 0 0

0 0 1 0 0 0 0 0 0]

. Hint: Try help diag and represent S as the sum of two matrices

having non-zero entries on different diagonals.

a) Compute S k for k=2,3,4. Describe in words what happens when computing S

k .

b) By using this reasoning, what do you expect S 11

to be?

c) As part of a linear algebra quiz, your friend answers 'TRUE' to the question: Is it true or false

that : If A*B=0 then one of the matrices A or B is the zero matrix? Based on your computations

above, do you agree with him?

PROBLEM 2: Suppose a linear transformation T has the property that T([1;3])=[5;4], and

T([2;1])=[3;6] where [1;3] is, as in MATLAB, the column vector with entries 1 and 2. Let A

denote the standard matrix of T.

Page 2 of 2

a) The information above tells you that there are matrices U and V such as 𝐴 βˆ— π‘ˆ = 𝑉.

Define U and V. Hint: read the problem until the end.

b) Using inv(U), V and matrix multiplication, compute A.

c) Verify that you have the correct A by computing in MATLAB 𝐴 βˆ— [1;3] and 𝐴 βˆ— [2;1] and

comparing with the values of T([1;3]) and T([2;1]), respectively.

d) Compute the expression det 𝐴 βˆ™ det π‘ˆ βˆ’ det 𝑉 . What general fact does this calculation

illustrates?

e) Compute det (𝐴 + π‘ˆ) βˆ’ (det 𝐴 + det π‘ˆ). What general fact does this calculation

illustrates?

PROBLEM 3: Let 𝐴𝑛 be the 𝑛 Γ— 𝑛 matrix with 1 on the main diagonal and 2 elsewhere.

a) For 𝑛 = 4,5,6 1. Use Matlab pre-programmed matrices (eye, ones, zeros) and matrix operations,

efficiently input 𝐴𝑛 .

2. Compute 𝐴𝑛 βˆ’1

and display the result with rational entries.

b) Propose a general form for 𝐴𝑛 βˆ’1

, expressed in terms on 𝑛. c) Check your theory for 𝑛 = 6.

PROBLEM 4: Consider the matrix A=[4,-2 ,1 ,5; 3, 8, 2, -1; 6, 8, 9, 2; 2, 3, -1, 0]. Compute the

following five determinants and comment what general properties of determinants your

computations at points b-e illustrate:

(a) det(A); (b) det(A T ) where

T stands for transposed; (c)det(A

2 ); (d) det(2 A); (e ) det (A

-1 ).

PROBLEM 5: The color of light can be represented in a vector [R; G; B] where R= Amount of

red; G= amount of green and B=amount of blue. The human eye and the brain transform the

incoming signal into the signal [I; L; S] where I – intensity, L –long-wave signal and S – short

wave signal and 𝐼 = 𝑅+𝐺+𝐡

3 ; 𝐿 = 𝑅 βˆ’ 𝐺; 𝑆 = 𝐡 βˆ’

𝑅+𝐺

2

a) Find the standard matrix P of the transformation from input [R; G; B] to output [I; L; S];

b) Consider a pair of yellow sunglasses for water sports that cuts out all blue light and passes all

red and green light. Find the matrix A that represents the transformation incoming light

undergoes as it passes through the sunglasses;

c) Find the matrix for the composed transformation that the light undergoes as it first passes

through the sunglasses and then the eye;

d) Compute the change in the [I; L; S] output signal between the [I; L; S] output without and

with the yellow sunglasses if the initial [R; G; B] input is [20;35;40].

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