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Posted: 10/11/2004 3:34:29 PM EST
[Last Edit: 10/11/2004 5:23:14 PM EST by scottryan]
Since I cannot use subscripts and superscripts, superscripts are yellow and subscripts are red. Anyone who helps me with this and gets the correct answer will receive free AR-15 parts.

A is m x n and B is n x p. Two vectors x, y are orthogonal if xTy = 0. If V and W are subspaces V + W denotes the subspace spanned by V and W.

The T's are the transposed symbol.

1. Determine which Row(A), Col(A), Nul(A) = kernel of A, Row(AT), Col(AT), and Nul(AT) are in Rn and which are in Rm. Identify any that are equal and explain why.

2. Show that every vector in Nul(AT) is orthogonal to every vector in Col(A). Show that every vector in Null(A) is orthogonal to every vector in Col(AT).

3. Determine what Nul(AT) + Col(A) is. Determine what Nul(A) + Col(AT) is.

4. Show that rankAB is less than or equal to rankA. Show that rankAB is less than or equal to rankB by considering (AB)T.

5. If P is m x n invertible and X is n x m invertible, then show rankPA = rankA = rankAQ.

6. Prove that if V and W are three-dimensional subspaces of R5 then V and W must have a nonzero vector in common.

7. Use LU factorization to argue that a rank r matrix A always factors into a m x r by an r x n matrix.

8. If rankA = r, then explain why there is a collection of the columns of A which give an m x r matrix A' of rank r, and describe how to find those columns. Then look at that submatrix A' and explain why there is a collection of r rows in it that give an r x r submatrix A'' of rank r. Explain how to find those r rows.

9. Compute a change of basis (change in coordinates) matrix from e1, e2 to:

b1 =
7
5

b2 =
1
-5

and then the change in basis (change in coordinates) matrix from e1, e2 to:

c1 =
-3
-1

c2 =
1
-5

Then describe how these change of basis matrices can be assembled to give the change of basis matrix from the b basis to the c basis

10. If A is a linear transformation R2 ------> R2 such that in a basis b1, b2 of R2 this transformation has a matrix representation of the form.

a b
0 d

then tell what the action of A on b1 is, and explain why this is so.



Link Posted: 10/11/2004 3:36:36 PM EST
Take home test, huh?


Be back in a while, to see if i can figure this one out.
Link Posted: 10/11/2004 3:37:25 PM EST
[Last Edit: 10/11/2004 3:37:41 PM EST by Penguin_101]
23 to the power of 5
Link Posted: 10/11/2004 3:38:23 PM EST
[Last Edit: 10/11/2004 3:50:37 PM EST by gaspain]
can you copy and paste the original somewhere? or take a picture of the question and post the picture


uhhhh...is it just me or are you adding questions every few minutes

Link Posted: 10/11/2004 3:39:27 PM EST
[rodney]FOUR![/rodney]
Link Posted: 10/11/2004 3:40:08 PM EST


Link Posted: 10/11/2004 3:44:48 PM EST
[Last Edit: 10/11/2004 3:45:32 PM EST by BigT]
Do think that's air you're breathing?

Edited to add...

Have a cookie.
Link Posted: 10/11/2004 3:47:43 PM EST

Originally Posted By mtechgunman:
Take home test, huh?


Be back in a while, to see if i can figure this one out.



Yeah, and my teacher is from China and I can't understand a thing he says. Everyone is lost in the class.



Scott
Link Posted: 10/11/2004 3:47:53 PM EST
From my Chemistry question thread:



5. The answer to all math problems is 5.
Link Posted: 10/11/2004 3:53:19 PM EST

Originally Posted By scottryan:
Since I cannot use subscripts and superscripts, superscripts are yellow and subscripts are red. Anyone who helps me with this and gets the correct answer will receive free AR-15 parts.

A is m x n and B is n x p. Two vectors x, y are orthogonal if xTy = 0. If V and W are subspaces V + W denotes the subspace spanned by V and W.

1. Determine which Row(A), Col(A), Nul(A) = kernel of A, Row(AT), Col(AT), and Nul(AT) are in Rn and which are in Rm. Identify any that are equal and explain why.

2. Show that every vector in Nul(AT) is orthogonal to every vector in Col(A). Show that every vector in Null(A) is orthogonal to every vector in Col(AT).

3. Determine what Nul(AT) + Col(A) is. Determine what Nul(A) + Col(AT) is.

4. Show that rankAB is less than or equal to rankA. Show that rankAB is less than or equal to rankB by considering (AB)T.

5. If P is m x n invertible and X is n x m invertible, then show rankPA = rankA = rankAQ.

6. Prove that if V and W are three-dimensional subspaces of R5 then V and W must have a nonzero vector in common.

7. Use LU factorization to argue that a rank r matrix A always factors into a m x r by an r x n matrix.



geeeeez.........I think this is a trap.
Link Posted: 10/11/2004 3:54:34 PM EST
Maybe someone could tell you how but not show the answers?
Link Posted: 10/11/2004 3:54:52 PM EST
[Last Edit: 10/11/2004 4:04:57 PM EST by danno-in-michigan]
Sorry, never took the class and have no ideas. (Actually, a few of my math professors were Chinese too, so I may have taken the class and just don't realize it). Good luck.

Edited to add: Are you sure all the "T"s are "T"s and not upside-down Ts? (i.e., the orthagonal projection symbol).
Link Posted: 10/11/2004 4:04:33 PM EST
dude...your gonna fail college

Link Posted: 10/11/2004 4:04:50 PM EST

Originally Posted By Penguin_101:
Maybe someone could tell you how but not show the answers?



I have no clue what is going on in this class. I am not going to understand it anyway. I need help bad.



Link Posted: 10/11/2004 4:05:29 PM EST
Are you sure all the "T"s are "T"s and not upside-down Ts? (i.e., the orthagonal projection symbol).
Link Posted: 10/11/2004 4:06:10 PM EST

Originally Posted By danno-in-michigan:
Are you sure all the "T"s are "T"s and not upside-down Ts? (i.e., the orthagonal projection symbol).




They are the transposed symbol
Link Posted: 10/11/2004 4:07:44 PM EST
Never mind, I quit at subspaces. You ain't seen nothin' yet, though, wait until you get to double dual vector spaces.
Link Posted: 10/11/2004 4:13:20 PM EST
I highly suggest you use a "life line" before giving your final answer!
Link Posted: 10/11/2004 4:15:39 PM EST

Originally Posted By scottryan:

Originally Posted By Penguin_101:
Maybe someone could tell you how but not show the answers?



I have no clue what is going on in this class. I am not going to understand it anyway. I need help bad.






Give a man a fish and he eats for a day, teach a man to fish and he eats for life.

To get you through tonight maybe post the answers but tell him how so when the test comes he won't fail.
Link Posted: 10/11/2004 4:18:47 PM EST
Get a tutor. You won't learn anything if everyone gives you answers.
Link Posted: 10/11/2004 4:19:09 PM EST
[Last Edit: 10/11/2004 4:23:46 PM EST by gaspain]
heres my answer


MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMNE­8fZx3Zff8ENMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM­M
MMMMMMMMMMMMMMMMMMMMMMMMMMM#q?'...............................,?qNMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM
MMMMMMM­MMMMMMMMMMMMMMMMMMZ............................... '',^:;:?xy@MMMMMMMMMMMMMMMMMMMMMMMMMMM
MMMMMMMMMM­MMMMMMMMMMMMMZ............................... ''.,^:?+73xxx3yNMMMMMMMMMMMMMMMMMMMMMMMMM
MMMMMM­MMMMMMMMMMMMMMMq>...............................'...,,^:>?3ff88hENMMMMMMMMMMMMMMMMMMMMMMM
MMMMM­MMMMMMMMMMMMMM@...............................''''.....,,,^^=7ZhhhqHMMMMMMMMMMMMMMMMMMMMMM
MMMMMMMMMMMM­MMMMMN@............................... ' '''''''''.......^;+Zfhhq#MMMMMMMMMMMMMMMMMMMMM
MMMMMMMMMMM­MMMMMMf............................... '''''.,,,,,,..''''''''''''',:3yfhhhMMMMMMMMMMMMMMMMMMMMM
MMMMMMMMMMMMMM­MMy, ................. ''''...,,^^::^^^,,,....'' '' '''.;xZfhh8MMMMMMMMMMMMMMMMMMMM
MMMMMMMMMMMMMM­ME? .................' ''...,^^^^^^^,,,.....''''' '''':=7ZhhfMMMMMMMMMMMMMMMMMMMM
MMMMMMMMMMMMMMMZ:^>3;:'...,^^^^^^,^^,,,^,,.''.,,.'...'^$qqhyEHMMMMMMMMMMMMMMMMMM
MMMMMMMMMMMMMM­Mh7+x$x+,..,,,,,^,,.^^^,,,,.'. '''. .^,Z@@8x@HMMMMMMMMMMMMMMMMMM
MMMMMMMMMMMMMM­Mqx7$yhZ=,'',=ZqH@@y^^;>>??>>,$8@HNq7?.,>h#Hh?##MMMMMMMMMMMMMMMMMM
MMMMMMMMMMMM­MMMM8x7f@HM=Z#MMMMMMMMEx===7+++EMMMMMMMMM@' ?yy?E@MMMMMMMMMMMMMMMMMM
MMMMMMMMMMMMMMMM#­h+f@y^@MMMMMMMMMMMy=;,,,:?@MMMMMMMMMMM7,:7;E@MMMMMMMMMMMMMMMMMM
MMMMMMMMMMMMMMMMMHZ­Z^?xMMMMMMMMMMqqy3>.^ ;MMMMMMMMMMM#x?8xMMMMMMMMMMMMMMMMMMMM
MMMM­MMMMMMMMMMMMM#hh>+7MMMMMMMMMN3.:+hMM#8>,,yNMNNMMMMqqx+h#MMMMMMMMMMMMMMMMMMMM
­MMMMMMMMMMMMMMMMME3$>>:MHqq@HEhZ= x=hMMMMMM;3,:f#EhZ+$$Z338MMMMMMMMMMMMMMMMMMMMM
MMMMMMMM­MMMMMMMM#8x=::,7#HEZ>' ;?hNMM@MMM# ?, =3333y73y8NMMMMMMMMMMMMMMMMMMMM
MMMMMMMMMMM­MMMMM#y;:??>?::^^::>=3E^fNMMyMMMM^:?33733x33$ZyyHMMMMMMMMMMMMMMMMMMMM
MMMMMMM­MMMMMMMMMMHZ$37=?3xyhq@q8y.^hMMMEMMMM;3yfyfy$7=$yfh8NMMMMMMMMMMMMMMMMMMMM
MMMMMMMMMMMMMMM­MMMM#Eqyx37=>;>fy$' =8Hq:y8#8':+$Zx===xfh8E@MMMMMMMMMMMMMMMMMMMMM
MMMMMMMMMMMMMM­MMMMMMMMM#HHqZ7:3xy'' ^ .=Zy>$yEN#HNMMMMMMMMMMMMMMMMMMMMMMM
MMMMMMM­MMMMMMMMMMMMMMMMMMMMMH3hq#>',:^ :'''+''>Zq8@HMHHE#MMMMMMMMMMMMMMMMMMMMMMM
MMMM­MMMMMMMMMMMMMMMMMMM@#HNMMhHqf':^:>;,'.^^'?;:$HMN#q@EHMMMMMMMMMMMMMMMMMMMMMMM
MMMMMMMMM­MMMMMMMMMMMMMM@EqE#NNEEEf8ffZ>yZ3;8+yhfxhN#HZEqHMMMMMMMMMMMMMMMMMMMMMMM­
MMMMMMMMMMMMMMMMMMMMMMM@qhf8H#773Zqyfy?f3­37H8qq@@N@H@xqq#MMMMMMMMMMMMMMMMMMMMMMM
MM­MMMMMMMMMMMMMMMMMMMMM#hZ3$q8MMMEyqqqHZ8fZ$@Eq­8EZZZZ>8ENMMMMMMMMMMMMMMMMMMMMMMM
MMMMMMMMMMM­MMMMMMMMMMMMH8x==7+>7y@833yf=xxxfhyZZfh3x$7qHMMMMMMMMMMMMMMMMMMMMMMMM
M­MMMMMMMMMMMMMMMMMMMMMMMq3=+>?=7xyEEq8f8qqq$3xZy3yx$y$@NMMMMMMMMMMMMMMMMMMMM­MMMM
MMMMMMMMMMMMMMMMMMMMMMMMMEZ+>;>?+$3xZyyyff8hx$ZZ$ZZZZfMMMMMMMMMMMMMMMMMM­MMMMMMMM
MMMMMMMMMMMMMMMMMMMMMMMMMMN8x;;>>?773337xxx3xx377$yyy@MMMMMMMMMMMMMMMMMMMM­MMMMMM
MMMMMMMMMMMMMMMMMMMMMMMMMMMMMq$3>,^,,,,,...,:>+3x$f8HMMMMMMMMMMMMMMMMMMMMMMMMMMM
MMM­MMMMMMMMMMMMMMMMMMMMMMMMMMMMMM3=;^,,,,,.:?7$yfNMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM
MMMMM­MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM#@Eq8hfHNMMMMM­MMMMMMMMMMMMMMMMMMMMMMMMMMMMMM
MMMMMMMMMMM­MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM­MMMMMMMMMMMMMMMMMMMMMMMM

Link Posted: 10/11/2004 4:19:32 PM EST

Originally Posted By Penguin_101:

Originally Posted By scottryan:

Originally Posted By Penguin_101:
Maybe someone could tell you how but not show the answers?



I have no clue what is going on in this class. I am not going to understand it anyway. I need help bad.






Give a man a fish and he eats for a day, teach a man to fish and he eats for life.

To get you through tonight maybe post the answers but tell him how so when the test comes he won't fail.



Please do. Your help is appreciated.
Link Posted: 10/11/2004 4:22:24 PM EST

Originally Posted By scottryan:

Originally Posted By Penguin_101:

Originally Posted By scottryan:

Originally Posted By Penguin_101:
Maybe someone could tell you how but not show the answers?



I have no clue what is going on in this class. I am not going to understand it anyway. I need help bad.






Give a man a fish and he eats for a day, teach a man to fish and he eats for life.

To get you through tonight maybe post the answers but tell him how so when the test comes he won't fail.



Please do. Your help is appreciated.



I have no idea, I just want people to tell you how and give you the answer. I know how you feel with a teacher that gives you work and dosn't explain how to do it or what it is. I have never had the language problem though!
Link Posted: 10/11/2004 4:24:20 PM EST
Me no rikey!
Link Posted: 10/11/2004 5:31:05 PM EST

Originally Posted By Penguin_101:

Originally Posted By scottryan:

Originally Posted By Penguin_101:

Originally Posted By scottryan:

Originally Posted By Penguin_101:
Maybe someone could tell you how but not show the answers?



I have no clue what is going on in this class. I am not going to understand it anyway. I need help bad.






Give a man a fish and he eats for a day, teach a man to fish and he eats for life.

To get you through tonight maybe post the answers but tell him how so when the test comes he won't fail.



Please do. Your help is appreciated.



I have no idea, I just want people to tell you how and give you the answer. I know how you feel with a teacher that gives you work and dosn't explain how to do it or what it is. I have never had the language problem though!



It is really fustrating.
Link Posted: 10/12/2004 3:39:09 AM EST
anyone?
Link Posted: 10/12/2004 3:47:34 AM EST
Sorry man, my matrix was 3-4 years ago, and now I let "R" do ALL my matrix work. I will shoot myself before I hand-crank matrix problems

shooter
Link Posted: 10/12/2004 3:52:38 AM EST
[Last Edit: 10/12/2004 3:56:41 AM EST by Red_Beard]
You can use _ for subscripts and ^ for exponents

so x_1 is x with a 1 subscript

x^2 is x squared


for the upside down T, hold down alt and type 193 ... you get



for the transposed matrix, you could do A^T


Link Posted: 10/12/2004 3:54:03 AM EST
I used to get help on math problems in one of the #math chatrooms on IRC
You probably won't get much of a response if you just start posting homework questions and ask someone else to provide solutions. If you work through the things and ask about parts that you don't understand, you'll get a decent reply.

Link Posted: 10/12/2004 4:00:29 AM EST
[Last Edit: 10/12/2004 4:05:33 AM EST by hepcat85]

Originally Posted By AeroE:
Never mind, I quit at subspaces. You ain't seen nothin' yet, though, wait until you get to double dual vector spaces.




Oh yeah, and wait till you get to double dual secret vector probation spaces!

Link Posted: 10/12/2004 4:16:21 AM EST

Originally Posted By scottryan:
anyone?



Sorry, I can't help on this one. What you might do is try going to the Engineering/Math library at your school and grab all the textbooks on this subject and start seeing if any of them solve these problems (or similar problems) as examples. Sometimes I was forced to resort to this method to do my homework in a class on complex numbers. You'd be amazed how often this method works.
Link Posted: 10/12/2004 4:26:20 AM EST
my brain hurts just lookin gat that shit
Link Posted: 10/12/2004 4:26:24 AM EST

Originally Posted By danno-in-michigan:

Originally Posted By scottryan:
anyone?



Sorry, I can't help on this one. What you might do is try going to the Engineering/Math library at your school and grab all the textbooks on this subject and start seeing if any of them solve these problems (or similar problems) as examples. Sometimes I was forced to resort to this method to do my homework in a class on complex numbers. You'd be amazed how often this method works.




ha ha ha

I used to do that one to for a topology class. Damn homework was too hard.

Another technique is to hunt around on the web for course websites at other schools where they're using the same text book (or even just courses on the same subject). A lot of times, the teachers will post solved problems on their websites.

Link Posted: 10/12/2004 4:31:54 AM EST
I am in differential equations and I thank God that this is my last math class and I don't have to take linear algebra. Calc 3 was intro enough to linear algebra to know that I don't want anything to do with it. Good luck.
Link Posted: 10/12/2004 6:18:59 AM EST

Originally Posted By Red_Beard:
I used to get help on math problems in one of the #math chatrooms on IRC
You probably won't get much of a response if you just start posting homework questions and ask someone else to provide solutions. If you work through the things and ask about parts that you don't understand, you'll get a decent reply.





I have no idea how to start them.


Scott
Link Posted: 10/12/2004 6:29:07 AM EST
[Last Edit: 10/12/2004 6:29:36 AM EST by Witch_Doctor]

Originally Posted By Cleatus:
my brain hurts just looking at that shit



+1 I'm terrible at math
Link Posted: 10/12/2004 6:31:00 AM EST
Linear alegra is kind of fun. I like computational math like that. It's like a big puzzle.
Link Posted: 10/12/2004 6:48:58 AM EST
Lessee...matrices were back in 1992 for me, so I won't be any help.

But I will tell a funny story about my class in Calculus of Several Variables.

In walks the teacher, and he's straight off the boat from China. I'm figuring he was at most an associate professor, and maybe not even that.

"Nah, Ah em uh litter hodd oaf healing, zo, uhspeek opp." Honest to goodness, that's the first thing he said. Read it out loud, and you might be able to figure out that he was saying, "Now, I am a little hard of hearing, so speak up."

I think it's a rule in college that Asian professors and teaching assistants must wear the cheapest dozen-for-a-dime awful dyed tennis shoes made. Which this guy wore. A few days into class, he wore - I am not making this up - one blue and one green shoe.
Link Posted: 10/12/2004 8:17:41 AM EST
It is so hard to understand when English is not the language of your professor. It is just a heartbeat and a mouth presenting material. Sometimes they have to trasnlate from Chinese to English in their head to figure out what they are going to say in English.


Scott
Link Posted: 10/12/2004 8:48:45 AM EST
Yeah it's a big ripoff since you're paying for a shit course.

The ones that really piss me off are the professors who've been teaching in the US for years,while speaking such shitty english that few people can understand their words, let alone the ideas they're trying to convey with those words.

You'd think someone hard working enough to become a tenured professor in in a technical field would invest a couple of hours a week in learning to speak clear english.

Link Posted: 10/12/2004 4:57:10 PM EST
anyone
Link Posted: 10/12/2004 7:10:20 PM EST
Yes I can do them however Im really busy w school this week

1. When is it due
2. What AR parts
3. Can you send me a scan because I can't read that red and yellow BS
Link Posted: 10/12/2004 7:15:43 PM EST
Link Posted: 10/12/2004 7:21:46 PM EST
My answer would be 42.

This is a great thread topic. btt
Link Posted: 10/12/2004 7:23:15 PM EST
i aced differential equations wedge if you have questions, but unfortunately the year i entered my engineering program i wasnt required linear algebra, but got to take discrete mathmatics instead. Computer Engineers have to take linear algebra now though.
Link Posted: 10/12/2004 7:29:24 PM EST
[Last Edit: 10/12/2004 7:32:35 PM EST by david_g17]

Originally Posted By jblachly:
Yes I can do them however Im really busy w school this week

1. When is it due
2. What AR parts
3. Can you send me a scan because I can't read that red and yellow BS



yeah, what he said, i think i still have my linear algebra book.

what's "Nul()"?

everything else i think i remember, but i don't have a clue what Nul is.

is it like elements which are zero (like null)?
Link Posted: 10/12/2004 7:35:43 PM EST
I'm going to send a copy to some Russian masters of math in Siberia and see what they come up with...
Link Posted: 10/12/2004 7:47:49 PM EST
Man, it's been a while.

A few pointers:

Vectors are orthogonal if their dot products are zero. You can say that a dot product measures the "advance of a in the direction of b". If the dot product is zero they're pointing at right angles to each other. (The concept becomes tricker in N space, which is why orthogonal is defined like it is.)

If the nul(a) stuff means the entries in A are all zero, it's easy to show that the vectors are orthogonal, since the dot product is always zero.

the rank(AB) stuff just falls out from the definition of matrix multiplication. If you know the dimensions of the two starting matracies you can determine the size of the matrix of the resulting matrix.

The subspace stuff relates to the basis. The basis is a set of vectors that let you describe any point in the space. Think of axes. Those form one possible basis for a space. You can have many other possible axe; rotate the axes, uses axes that aren't orthogonal, etc. The outline of the solution would be to show that if both have basis that span the space each can be described in terms of the other.

Link Posted: 10/12/2004 7:56:36 PM EST
Holy Crap!
You mean I am not the only poor sucker who is forced to take Linear Algebra?
WOW.

Oh, and I am in the same boat you are, except my ta was french, but he is getting switched, somethin' about his visa? I knew I should have stoppeed makin those calls to the INS. . . .
Link Posted: 10/12/2004 8:03:51 PM EST
I'm glad my undergrad degree was in criminology. Talk about easy. Hmm, maybe that's why cops shoot so many dogs...

But, seriously, that looks like some hard crap to do!
Link Posted: 10/12/2004 8:05:08 PM EST
Hmm.....I'm in linear algebra right now, and while I could probably do those, it'd be a royal bitch to try to explain whats going via posting here, and I've got a moral code that prohibits me from doing other people's work for them (mostly that code is called laziness).


I'd HIGHLY suggest you find a fellow student in the class to tutor you, or find someone who took the class recently.


BTW, what is the textbook for that class? We're using Linear Algebra and its applications 3rd Edition, by David C. Lay -- its fairly easy reading (for a math book) with enough worked out examples that even if your prof / TA is completely useless, you should be able to learn enough to pass tests.
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