MATH1051: Calculus and Linear Algebra. Questions and Answers

Student: r u avaiable for consulation besides monday and friday during exam period??

AK: Yes, come and see me.

Student: for finding critical pts/abs min or max, do you firstly find the deriv. then find critical pts, then use 2nd der to see whether they are max or min (x>0 min, x<0 max). if then ask for abs min or max then sub critical pts and any end pts if given in f(x) to compare, if so it didn't work for a question in the june 99 paper!! please help

AK: Bring me the question.

Student: Hi, I was reading one of the questions posted by another student in the forum where he said that he wrote 'for the error to be less that 10^-10, the sum must be consistent to the 10th term' for his matlab assigenment and got 2 marks deducted. Just to let you know, I was also taught the same thing at my high school back home. It is definitely a faster method as we can get the answer just by observation and without any calculations as the tutors and maybe lecturers expect us to do. For the record, I also got 2 marks deducted, but I'm not fussed as it is only 1%. And btw, thanks for being a great lecturer all this while. And thanks also for always being available for consultation.

AK: You are welcome.

Student: regardin the taylor series for 1/x right, if you are doing it from 1st principle, you have (x-a)^n/n! right, but if you assume 1/x as 1/(1+(x-1) then you miss the factorie please help

AK: No, we do not miss anything. Come and see me.

Student: i sent an e-mail to mike about this but he didn't respond, so i will ask you. i was looking at my marks outside mike's office and i noticed that about five of my marks are missing. i have handed everything in. do you know why this might be?

AK: Bring your assignment papers to me.

Student: How do you calculate the integral of [(ln x)^2]/x ? If you use integration by parts, what is the derivative of (ln x)^2 ? Thanks

AK: I would use substitutions. Let u = ln x. Then du=dx/x. I leave the rest for yourself.

Student: Hey Abdulla, I have done all of the past exam papers. And I just have one question to ask you... There is a question on one of the past papers asking for the radius of convergence for the Taylor series of y=(1/x) about x=1. Now, the answer I got for the Taylor series is :- 1 - (x-1) - (2(x-1)^2)/2! + (3(x-1)^3)/3! - ..... Is that the correct Taylor series for (1/x)? If so, how do you find the radius of convergence for it? Many thanks.

AK: The series you have got is very close to the correct answer. First note that 1/x = 1/1+(x-1) = 1-(x-1)+(x-1)^2-(x-1)^3+...

This series is valid for |x-1| < 1, or 0 < x < 2. So the radius of convergence is 1.

Student: I know that tommrow is the last day before the beginning of the exam block for the first semester. And you may not be there for any consultations. But would it be OK if I come up there to ask you a question from one of the past papers? Thanks a lot.

AK: Sure.

Student: Hey Abdulla, I have a quewstion about the marking scheme. Please tell if this is correct.

10% - Tutorial sheets

10% - Matlab Assignments

20% - Mid Semester Exam

60% - Final Exam

AK: That is correct.

Student:

1 0 2 :0

0 0 1 :0

0 0 0 :0

x + 2z =0

z = 0

is y = 0 ?

do we put z = A and y = A

x -2A -2

y =( A ) =A( 1 )

z A 1

is this the correct e vector?

AK: Since z=0 it follows that x=0. But y=alpha, an arbitrary number. So the e-vector is (0,alpha,0)^t = alpha (0,1,0)^t (t for transpose) .

Student: You previously mentioned in the forum, that we can use the binomial expansion to calculate (x-2)^-1. How do we do this if we only know the expansion for (x+1)^a ?

AK: Note that (x-2)^-1 = (-1/2)*(1-x/2)^-1.

Student: i realised that you're suggested something for find the maclaurin series for x/(2-x), just for a change, can you do: x/2(1/1-x/2) and solve from then on?? Knowing series for 1/1-x Can we come and see you during the exam period??

AK: Yes, you can.

Student: Hey Abdulla, would you do me a huge favour? Could you please put the notes for the last 2 - 3 lectures of the semester where you went through some exam questions on the net? Thanks

AK: I've got those slides here in my office. You may come and get them.

Student: I was looking at some of the previous exam papers in the library, and some of them contained formula sheets with all the trig identities that we were "supposed" to have been taught in high school, as well as some common integrals. Do we get a formula sheet like that? Thanks

AK: As I said before you would get a formula sheet.

Student: Sir, in the exam, when we're asked a question on absolute convergence and interval of convergence, do we have to write out the proof whether the end-points are convergent and what type of test? or do we merely just write down the name of the test eg: Alternating test, nth term test ... etc.? Thank-you

AK: You should always check the end-points. It is enough to write the name of the test you are using.

Student: Do you know of any extra examples or resources on planes. I have been trying to figure out how to do the example in the typed lectur notes from your web site on page 96 and can not figure out how to get the n=3i+5j+4k

AK: To obtain the orthogonal vector to the plane containing vectors v and w you need to find the cross product of v and w. If you need more help please come and see me.

Student: Mike went through questions on the exam which were

infinite series

MS and TS

Intergration

Vols of rotation

Increasing decreasing functions-max/min

Angles between vectors

LI vectors

Gaussian elimination

e-values

I think that was about it.

Are there going to be other questions aswell? Just so I am prepared!

With the second Matlab Assignment will we be able to obtain the marks for these at some time?

Thank you for all your help. Enjoy your time in the USA and hopefully we will be able to see you in some future years.

AK: Ask Mike your first question. Your marked matlab test 2 papers will be placed in Level four next to Mike's office.

Student: What are you planning on doing in USA. By the way would I be able to come and see you on the 'studying week' before the exam block. Cause I have some problems from the past exams. many thanks

AK: Sure, come and see me.

Student: if we have a evalues of 1 with a multiplicity of 2, does it means that we will have 2 e vectors for e value of 1?

AK: Yes, It does.

Student: what do it mean when a matrix A is Singular? how do u find c if the matrix A is singular? A=[1 1 1] 0 c 2/3 3 0 c

AK: A matrix is singular if det(A) = 0. From this you can find c.

Student: Are we still allow to bring our own piece of formula sheet which you had mentioned earler to the examination?

AK: No, your are NOT.

Student: I was looking at the past exam papers and some of them have a list of calculus formulas. Do we get that too?

AK: Yes, you do.

Student: will you still be available for consultation and/or continue to answer questions on the forum during swat vac and exam period before the test??

AK: The forum will be open until 17/6/2001. But if students have any questions they just need come and see me.

Student: With marks outside Pemberton's office, I am missing tutorial 7's mark. Tutorial 7 was the tutorial in which my tutorial was on a public holiday (monday). I left my tutorial under your door on the Friday. Was it marked? If so can the mark be put into the system. My ID is 40117708, thanks.

AK: I have passed all the papers to Mike. So talk to him.

Student: These are the eigen values I had for the results of Problem 3 for MatLab Assign. 2. How can some of the values turn out to be complex?

ans =

1.158

0.1004 + 0.50003i

0.1004 - 0.50003i

-0.45661 + 0.39688i

-0.45661 - 0.39688i

-0.4456

AK: The eigenvalues of a matrix are sometimes complex numbers.

Student: Abdollah, I noticed that the MATH 1051 results are currently posted outside Mike's office. When I checked my marks, I discovered that there were 3 spaces with no marks. They were under columns 1, 6 and 12. I am assuming that columns 1 and 6 correspond to tutorial sheets 1 and 6, whereas column 12 corresponds to the first Matlab assignment. If this is so, then I'm a little confused, as I've already handed in all of the listed (1,6,12) assessment. I have actually been given back these two tutorials (1 and 6) with marks allocated for each, however, I have not managed/can't seem to find my Matlab assignment outside Mike's office. I was just wondering if there was anything I can or am able to do to fix up my final marks? because it's not quite right knowing that I handed something in, had it marked and given back to me, and then didn't have that mark recorded down. Am I able to see you or something to fix this up? Thanks.

AK: Yes, come and see me.

Student: dearest AK, do we only have to pass the final exam to pass the subject?

AK: Dearest student! The final exam worth only 60% of the final grade. Have you ever read math1051 subject profile which is in my web site?

Student: i don't believe that mike is going to give us the solutions to the past exams, i'm having great difficulty with it please help

AK: Come and see me.

Student: hi, i am doing the revision question and i am confuse whether o leave the x alone or deal with it some how. the question is find the maclaurin expansion for x/(x-2). i try to use binomial expansion x(x-2)^-1, but what about x? thanks

AK: First find the binomial expansion for (x-2)^-1 then multiply that by an x. Now you have a series for x/(x-2). See me if this does not help you.

Student: What happned to all of the other (non math related crap) on this page?

AK: I could put them in this site but some students emailed me asking to keep this page just for math questions. I know this page is very boring now. Fortunately this is the last week of teaching and you do not check this boring site after a couple of weeks anymore.

Student: When are you available for any consulting? Because I came to your office yesterday during the contact hour, and ended up waiting for you for more than an hour. But you never turned up. And the guy inside said that you went out for lunch and should be back within a few minutes. Whats going on? So,I don't want to wait till Friday to come and see you, so can you arrange another time for me to come and talk to you about some of the questions I have. It would be great if you could arrange a time slot during Wednesday or Thursday afternoon. Thanks a lot.

AK: Well, yesterday was Tuesday and my consultation hours are on Monday and Friday. If you are talking about Monday afternoon I had an appointment and couldn't come back on time. Come to me any time you like. You may ring 52302 from inside uni and check with me before you come.

Student: Abdollah, I would just like to say thankyou for all the help that you have given to us poor students who don't really understand Mike Pemberton's numbers that he writes in mid-air. Thankyou for making the mathmatics clear and simple (as can be anyway!). Hope you get on well in America and thankyou again for putting the mathmatics in a simple perspective.

AK: You welcome. I really enjoyed teaching MATH1051 this semester.

Student: in a lecture last week,mike explained what the "or otherwise" meant. However, my friends and i are arguing over what he actually said. could you please clear this us for us? -> do we use another computer program to solve (eg excel) or can we do it by hand? TA,

AK: I talked to him about this. You are not allowed to use excel to do the calculations. So all the calculations should be done in Matlab. But you may use excel to draw table of the results.

Student: Hey Abdollah, I'm a bit confused about Cramer's Rule. I understand how to find the cofactors, however I do not understand how to change the order of the matrix that we need to multiply with 1/det(A)???? Thanks. Also, how come you are not teaching at UQ next semester? Who will look after the forum??

AK: To form A inverse you need to put the cofactor corresponding to position (i,j) in position (j,i). If you need more help come and see me.

Student: Sir, how do we find the inverse of x+cosx? and x^3+x+1?

AK: We cannot find explicit inverse functions for these two. However we can prove there is an inverse for each since f' is positive.

Student: hi, i have been trying to revise on limits, how do we solve (9-t)/(3-t^(1/2)) as x approach 9. thanks

AK: If we sub 9 for t it become 0/0 so we may apply Hopital's rule. I leave that for you.

Student: hi sir, can you please explain to me what is bound above and bound below and in the case of a(n)=(2n-3)/(3n+4). thank you

AK: Your question is not very clear. However if we assume n >= 1 then

-1 < (2n-3)/(3n+4) < 1. -1 is a lower bound and 1 is an upper bound for a(n).

Student: in one of my revision section 12.10 question 47. they ask to use series to evaluate the limits as x approach 0 for (sinx-x+(1/6)x^3)/x^5. and just for interest, how many lecture do you teach this week for math1051 and can you give me the time please, it will be appreciated. thanks

AK: I'll teach Wednesday (two hours), Thursady and Friday.

Student: hi, i just want to aks that is last year exam paper good for revise purpose? or can you give me topics that will be test in more specific. when you say everything it is too general and i am afraid if i left out some of the important one. thanks heaps for your help.

AK: Last exams are quite good for revise purposes.

Student: can you or mike answer a question that has been the vain of my existance for more than a year now?. What is the intregal of e^(sinx) ? if you can help me, post it here, or send me an email @ subtlenasha@hotmail.com I really hope you can help, coz i really can't solve it and i have been trying to for a really long time now.!!!! thanks sarah.

AK: No, I cannot do it. I also like to see the solution of this integral.

Student: just wondering if there is tutorial this week?? and if not, how will we get back our marked week 10 problem sheet?

AK: There is no tutorial this week. The marked problem sheets 10 will be placed in Level 4 next to Mike office, I guess.

Student: Is there a problem sheet 11, if so can you put it on your website, also in the final exam will there be a formula sheet for trig identies etc?

AK: As soon as I get the problem sheet 11 from Mike I'll put that on my website. Ask Mike your second question.

Student: what is the matrix given in the matlab test 2?

AK: I am sick of answering questions on matlab assignment two. Please stop this topic.

The matrix is

L = [0, 1.21, 1.59, 0.97, 0.73, 0.42;

0.51, 0, 0, 0, 0, 0;

0, 0.73, 0, 0, 0, 0;

0, 0, 0.85, 0, 0, 0;

0, 0, 0, 0.89, 0, 0;

0, 0, 0, 0, 0.62, 0];

Student: Hey Abdulla, In the Math1051 lecture today Mike Pemberton said that the question in the Matlab assignment where it asks what happens to the population eventually, refers to finding the eigenvector that corresponds to the largest eigenvalue of the Leslie Matrix, and relating that to the Populations. Now when I go to use Matlab to find this eigenvector it keeps giving me the Identitiy matrix. What does this mean? Does it mean that the population goes to zero? If so that can't be right. The code I used was:

L = (The leslie matrix given in the question)

eig(L)

e = (The lagest value from eig(L))

I = [1 0 0 0 0 0;0 1 0 0 0 0;0 0 1 0 0 0;0 0 0 1 0 0;0 0 0 0 1 0;0 0 0 0 0 1];

E = L-e*I

RREFMOVIE(E)

The row reduced echelon form always comes out as the identity matrix. Where am I going wrong? Help me!

I also have another question. Its probably been asked before so I'm sorry if you have to repeat yourself. In question 3 is the breeding rate taken from question 1 or from question 2. Well thats all. Thanks ^_^

AK: I guess you'd better ask Mike your first question. My suggestion is to solve the questions in Matlab assignment 2 without using eigenvalues and eigenvectors.

With regard to your second question if I were you I would do Part 3 for breeding rate taken from Part 1 AND from Part 2.

Student: Thanks for replying my question, what's the matrix given in the matlab test 2?

AK: I did not get this. Are you complaining or thanking? Let's be positive. I take it as thanks.

Student: Could you please post the Matlab exercise/worksheets onto your site? Our tutor says there's a sheet 5, but there aren't any in the room.

AK: I have no idea what you are talking about.

Student: Actually, I don't get an equilibrium in part 2, whether the breeding rate is 0 0 1.59 0.97, etc I get random increases and decreases each year...?

AK: Something is wrong with your calculations, I guess.

Student: Hey Abdollah,thanks for all the help you give especially your speedy reply time on the forum. Could you please explain how you find the equation perpendicular to the plane formed by the three points of a triangle. In the lecture notes all it said was the equation equalled AB*AC etc. Thanks.

By the way, with the MATLAB assignment, I used the breeding from part 2 because this way, the population eventually goes to zero since the percentage increase is a negative value. Does that sound right?

AK: I have put the solutions to Tute Sheet 10 questions on my web. If that did not help you with regard the question you asked then let me know.

About matlab assignment Part 3, you are right. If we use the breeding from part 2 the population eventually goes to zero since the percentage increase is a negative value.

Student: About the matlab assignment, for the first part, i've got the % increase to infinity as someone mentioned before, but for the second part my % increase varies, it goes up for some years and decrease for the remainder , and for the last part, my % actually decreases. Am I doing somethin wrong??? If so please help (for the 2nd and 3rd, i only adjusted my Leslie matrix)

AK: I guess something is wrong with your calculations.

Student: about part 3 of the matlab assignment,just to make sure, do we take the breeding rate from the beginning of the question, ie0 1.21 1.59....0.42?

AK: I think so.

If we take the breading rate as part 2; that is

0, 0, 1.59, 0.97, 0.73, 0.42

then there is an equilibrium percentage. Am I right?

Student: I noticed that people have been asking about the equilibrium populations for the Matlab assignment. The assignment doesn't ask for this, it asks for the equilibrium in the percentage population increase. According to my calculations, all three scenarios in the assignment result in positive equilibrium percentages, meaning that in all three scenarios the populations increase to infinity. Is this correct?

AK: Yes, that is correct.

Student: I can't find Leslie matrices in the maths notes...! What are they!?

AK: Do not worry about the name. Just pick the matrix given in matlab test 2 and multiply that by itself many times.

Student: What is Leslic Matrices?

AK: The matrix given in your matlab test 2 is a Leslie Matrix.

Student: hey abdulla, good work mate. the forum was very helpful and it is good that you take the effort to answer questions. Good stuff

AK: you welcome.

Student: We belong to tute Tf (Tuesdays, 12-1pm). We didn't have a tutor for our first tutorial and you came and collected our solutions. We have never received them back. Are they marked? Our tutor is Helen Parker.

AK: I passed your papers to Mike. I you didn't get a satisfactory answer from Mike about this come and see me please. Have you ever talked to Helen about your papers?

Student: Can rows be exchanged when doing the Gauss-Jordan thing to find inverse matrices?

AK: Yes, they can.

Student: Hi, i am enroled in this subject late and i start to hand tutorial problem sheet 2, that is mean that if problem sheet 11 is not going to be mark, can you mark it for me to make the total out of 10 or do i loose one problem sheet mark? thank you very much.

AK: I am afraid you loose one problem sheet mark.

Student: for the end semester exam, do we know what type of question and which topics, or can be ANYthing. do you know how many question are there? cheers

AK: All the topics could be in the final exam. I do not remember the number of questions.

Student: sir, in question three in the problem sheet 10. how do we approach it? if we use the rate of the pipe and add to another rate of another pipe, then the answer must be the rate too, but instead we have hours, how can we make it make sense. thanks

AK: You form the following system of equations:

8xa = V

6xa + 6xb = V

10xb + 10 xc = V

What we are looking for is the time t such that

t (xa+xb+xc) = V. You may assume V (volume) is one m^3.

Student: Dear sir. for the problem sheet 10, question 4 ask to find values for k which are inconsistent and represented by Ax=b. how do we define when its has no solution? thanks

AK: I have answered this in this forum.

Student: What is a linear combination? and what is mean by vectors v(1), v(2), v(3)...v(m)span V? thank you very much.

AK: We say the vector v is a linear combination of vectors v1, v2, v3, ..., vn if

v = a1v1+a2v2+...+anvn, where a1, a2, ..., an are numbers.

We say v1, v2, v3...vm span V if any vector v in V is a linear combination of v1, v2, ..., vm.

Come and talk to me if did not make any sense.

Student: this question regarding the exam, have you ask Mike if we allow to have one A4 of anything to bring in the exam? are we going to know specific topics for each exam question like the mid semester?

AK: Yes, I spoke to Mike and you are NOT allowed to bring any paper with you in the exam.

Either Mike or me will talk about the format of exam next week.

Student: can you explain to me clearer what is a vector space? and i don't get the bit about i, j, k. what are they for? is it important to know? thanks.

AK: Not in this forum. Come and see me.

Student: Dear sir, when is the last lecture for math1051? are you going to have a revision lecture? and is it right that we'll be tested on everything we did since the first week. thanks

AK: There would be a revision if we finish before the end of next week.

Yes, everything from the first to the last week could be in the exam.

Student: Dear Sir,

Are you actually telling us that there is no equilibrium population at all? This means that we won't need to answer some assignment questions at all. If you don't already know, I'm referring to MATLAB assignment 2 for the Leslie matrix

AK: I am sure that for first part of the question in Matlab assignment 2 there is no equilibrium population (population is actually going to infinity). I didn't check the other parts. If you change some of the figures then there might be equilibrium population.

Student: regarding sheet 10, Q7b, i get a row of zeros, does it mean that there is no solution??

AK: The matrix has an inverse. So you need to check your calculations. Come and see me if you couldn't find your mistake.

Student: Are you able to place your overhead lecture notes on your MATH 1051 website??? , because in many of your lectures, I was unable to copy down everything that was wriiten on them. THANKS!!

AK: Come and get them from me. I will not put them in my homepage.

Student: On the Matlab assignment 1, I wrote for my answers to the error parts, 'for the error to be less that 10^-10, the sum must be consistent to the 10th term' and whoever marked my paper said 'why can we do this with the error?' and deducted me 2 marks. The thing is, this is true fact, and the way I was taught at home so although it may not be a method taught here, how can it be marked wrong? While I'm not really too fussed about losing the marks as it is only 1%, I think that you should be aware of the problem, because it seems unfair that people can lose marks for quoting methods that are right, just unfamiliar to tutors. It is also hard because how do I know what methods have been taught at high school over here?

AK: Bring your papers to me. I'll fix your mark if you are correct.

Student: Dear Sir,

I know not if you are as up-to-date on the MATLAB assignments as Mr. Pemberton is, but he is too difficult to contact (he never replies to my emails) so I'll ask you. For assignment 2 I found the leslie matrix, and I started doing L^2*N, L^3*N etc. to hope to see if there was any 'equilibrium' population, but my populations kept on getting larger and larger!

AK: So there is no equilibrium population. Note that the number 0.86 should be 0.62.

Student: Is Problem sheet 10 the last problem sheet? If so thank god. If not WHY?

AK: There is also tute sheet 11 but you do not need to hand it to your tutor. That means it is worth 0% towards your final mark.

Student: So if we did our Computer assignment in excel, will we be marked differently than if we did in matlab? I find excel easier than matlab, all u have to do is fill the columns/rows with the numbers to make the leslie matrix, and then N use MMULT function to multiply matrices together etc. So would we just have to tell what we did in excel to get answers?

AK: I think so. You may want to check this with Mike.

Student: With Q1c on problem sheet 10, I keep getting 0x + 0y + 0w + 0z = 1. Am I doing something wrong, or is there a mistake in the question? Doesn't this mean that there is no solution? I tried solving it a number of different ways but it doesn't seem to work. Thanks

AK: I guess you have not done any mistake. And there is no solutions since by last row 0x + 0y + 0w + 0z = 1.

Student: With the next computer assignment, it says use Matlab or otherwise to set up... so do we have to use matlab or could we use say excel to do the assignment?

AK: I guess you can also use excel or maple for the assigments.

Student: I couldn't find my matlab assignment outside Mike's office. I looked through all of them at least 3 times. Where could it be? I don't know

AK: I guess no every paper has been marked yet.

Student: For problem sheet 10, Q 3, can you find A,B,C using matrices, and then find out what A+B+C equals? Also, do we have to do Q10 for the assignment?

AK: That is correct. No, you do not need to do Q10.

Student: Why is there are problem with putting the results on the web? It doesn't seem to be an issue in any other subject. Putting results on the web would be far more appropriate than just dumping the papers in the corridor where anyone can see not only your mark, but what exactly you did wrong. It's a bit silly- much like the discrepancies in marking. It's just incredible!! Maybe you should check how math1061 is run, it'll give you a few pointers!

AK: Talk to Mike about this.

Student: How do we do question 4 of the problem sheet 10? what does it mean by Ax=0? thanks

AK: See the following questions.

Student: on sheet 10, Q4, waht do they mean by inconsisent, and homogenerous solution???

AK: By inconsistent we mean no solutions. Homogeneous means right hand side of the equation is zero.

Student: For question 4 on problem sheet 10, I'm a little stuck, i don't suppose you can give me a hint? thanks

AK: Find Gauss row reduced form for the aug. matrix which is

1 1 1 2

0 2 -1 3

2 -4 k 4

Then write the corresponding equation for the last row. The system has no solutions if in the last row of the row reduced form you have

0 0 0 a,

where a is not zero.

Student: For question three problem sheet ten, do we use what we got and put it in a simultanous equation? like; A=8; A+C=6; B+C=10; A+B+C=x ? then use the Gauss elimination to solve this? thanks

AK: That is correct.

Student: is this all the question that we need to hand in? 1c, 3, 4, and 7b? is it? thanks

AK: I think so.

Student: Can you put the solutions to the mid-semester test and matlab 1 assignment on the web so we can see what we should have really done?

AK: I do not have the solutions. Talk to Mike please.

Student: Can you put up the last 5 or 6 slides for Thursday (24/5)'s lecture please?

AK: The scanner does not work. But I have a copy of my slides on my desk. You may come and get them and prepare your own copies.

Student: Will you be putting up all the marks for tutorial assignments. pracs., mid semester exam and final exam so the student can check to see that there is no error in the calculation of the final grade? You can just list the student's ID nos (no name). with the individual marks.

AK: I spoke to Mike about this and he did not agree. But if any student likes to see his (her) marks please come and see Mike or me.

You emailed this 7 times. Please do not email and email more than once. That wastes my time.

Student: I know that for a 1x1 matrix the determinent is the one number. But how would you go on about calculating the determinent for a 2x1 matrix. i.e. (1 2) or (3 4)?

AK: Determinant is only defined for SQUARE matrices.

Student: With Matlab assignment 2, is Leslie matrices a special case of Markov chains?

AK: I don't know. Ask Mike.

Student: Can you put past Math1051 exams on your website, so if students wish to go over similar questions to that of the real exam they can. Thanks!!

AK: I do not have them. If someone brings me a nice copy then I'll put it in my web site.

Student: Will you be putting up all the marks for tutorial assignments. pracs., mid semester exam and final exam so the student can check to see that there is no error in the calculation of the final grade? You can just list the student's ID nos (no name). with the individual marks.

AK: I'll check this with Mike and if he agrees I'll do it.

Student: Where can we get our matlab assignment 1 results from?

AK: Probably in Level Four, next to Mike's office in math. building.

Student: whassup man? i was just printing out the past exams and i was wondering if there was anyway to find out the answers of past exams cos i can do the questions but in the end they could be wrong? keep it cool. thanx.

AK: I don't know. Ask Mike.

Student: hi,

I can't believe the inconsistency in the marking scheme in maths. it is absolutely pathetic. you probably won't take this mail seriously, but i am serious, and i hope you can take some steps forward to fix the problem.

With matlab assingment, how the heck can some one get 11 out of 10. I saw an assingment for 10.5 out of ten. Do these tutors know what the hell they are making.

My paper has 7.5 and another guy who got 10 had exactly the same formula ( my one was marked wrong) and had exactly the same answers. Whats doing. Lucky it is only 5%.

I strongly hope you get this fixed. I am paying 600 odd dollars for this subject, and all i want is decent lectures (which i am happy about), competent tutors, and a fair marking scheme.

This fair marking scheme is a joke. Please do something about it. There is no escuse.

Thanks a lot.

AK: Mike and I are both are aware of the inconsistency in the marking scheme. This will not happen for the final exam. The final exam papers will be marked by lecturers and would be consistent since each part of a question is marked by only one lecturer.

If someone's mark is above 10 for the first matlab test we only count that 10 when the final marks are calculated. If there is any mistake in marking in someone's paper (assignments, Mid-semester test or Matlab test) please bring that to Mike or me, we will fix it. I know that does not solve the inconsistency problem but at list you do not get less than what you deserve. I have already corrected the marks for more than 15 students. So do not be shy and come to talk to us.

I guess the math dept should find a better solution for marking the mid-semester exams papers and the tests. But this is not in my hand.

Student: What is it actually asking, i don't really follow the question!!!

AK: It asks you to find two orthogonal vectors to v. There are many answers to this question.

Student: how do we do question 9 on tute sheet nine. i.e. if we assume that w.v=0 where w=(w1 w2 w3) and v-(1 1 1), wouldn't w1=w2=w3=0? What does this mean? -> is there only 1 solution?

AK: I have already answered this question in this forum. However, from w.v =0 we obtain w1+w2+w3=0.

Student: Could we get answers to the Matlab assignments and tutorial sheets, please?

AK: Solutions to the tuorial sheets are on my web. I may also put the solutions to Matlab assignments on this web.

Student: If we have any questions regharding any of the tute sheets is it possible for us to come and talk to you about them? If so, where is your room, and when are you available for any quiries?

AK: First check the solutions to the tute sheets which are on my web. If they do not help you come and see me. My office number is 703 in maths building.

Student: Can you please explain what Q.9 on problem sheet 9 is asking? Cheers.

AK: See the following question.

Student: For question 9 in problem sheet 9

How many sets of vectors do we need to use to make the basis? (is 3 sets enough)

Could there be more than one solution? Thanks!

AK: You need two vectors, say u and w. These two must be orthogonal to v=(1,1,1)^T; that is u.v=0 and w.v=0.

The answers {u,w} could be different. That means there are many different basis for this vector space. But all consist of two vectors.

Student: if we fail the matlab component, do we fail the entire course or can we make up for it in the other areas (tutes, exams)? and if we can, how much is the matlab component worth?

AK: Each Matlab test is worth 5%. So if someone even misses the two Matlab tests he (she) only loses 10%. It means he (she) still has a chance to get a 7 (which is 85% or above).

Student: If A, B, C are square matrices

A= (1,1; 1,1) B=(2 2;-1 -1) C=(3 4; -2 -3) then

A does not have an inverse because DET(A)=0, also AB=A

B does not have an inverse because DET(B)=0, also BA=0.

B^2=B

C has an inverse which is itself, C.C=I, AC=A then AC=AB since both AC=A=AB, shouldn't C=B! Can you explain this?

AK: Let A, B and C be three matrices. In general if AB=AC then we cannot conclude B=C. This is one of the differences between numbers and matrices.