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Posted: 10/11/2004 4:34:29 PM EDT
[Last Edit: 10/11/2004 6:23:14 PM EDT 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 AR15 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 threedimensional 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. 


Take home test, huh?
Be back in a while, to see if i can figure this one out. 

"T've got two guns, one for each of ya."
"Any you sumbitches calls me grandpa,.......... ...........I'll kill ya." 
23 to the power of 5



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 

just another sigline that nobody reads

[rodney]FOUR![/rodney]





On the plains of hesitation lie the blackened bones of countless millions who at the dawn of victory lay down to rest, and in resting died." (it ain't over till it's over)
Adlai E. Stevenson The 94 AWB is dead, but the war continues. 
Do think that's air you're breathing?
Edited to add... Have a cookie. 


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


From my Chemistry question thread:


"T've got two guns, one for each of ya."
"Any you sumbitches calls me grandpa,.......... ...........I'll kill ya." 
geeeeez.........I think this is a trap. 

"You know, it really aint so bad if you close your eyes and pray to God"
"get me a big bowl of PIE, some ice cream on it, mmm hmm good! Put some on your head! Your tongue would slap your brains out trying to get to it!" 
Maybe someone could tell you how but not show the answers?



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 upsidedown Ts? (i.e., the orthagonal projection symbol). 


dude...your gonna fail college


just another sigline that nobody reads

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


Are you sure all the "T"s are "T"s and not upsidedown Ts? (i.e., the orthagonal projection symbol).



They are the transposed symbol 


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



I highly suggest you use a "life line" before giving your final answer!


A well regulated militia, being necessary to the security of a free state,
the right of the people to keep and bear arms, shall not be infringed. 
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. 


Get a tutor. You won't learn anything if everyone gives you answers.


Common sense is a wonderful thing...it's just not common.

heres my answer


just another sigline that nobody reads

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! 


Me no rikey!



It is really fustrating. 


anyone?



Sorry man, my matrix was 34 years ago, and now I let "R" do ALL my matrix work. I will shoot myself before I handcrank matrix problems
shooter 


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 

I want to put methamphetamine vending machines in every school cafeteria.
 AR15fan 
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 want to put methamphetamine vending machines in every school cafeteria.
 AR15fan 
Oh yeah, and wait till you get to double dual secret vector probation spaces! 

â€śHey, Iâ€™ve been in a firefight before! Well, I was in a fire.
Actually, I was fired...from a frycook opportunity.â€ť â€śWashâ€ť Warren 
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. 


my brain hurts just lookin gat that shit



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. 

I want to put methamphetamine vending machines in every school cafeteria.
 AR15fan 
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.


plkhlyuhgudryszwsrtgfhyjikni67e4esrfvyujinjnul,u76e43e676yvuj
I'm Catholic. 
I have no idea how to start them. Scott 


+1 I'm terrible at math 


Linear alegra is kind of fun. I like computational math like that. It's like a big puzzle.


"All truth passes through three stages: first, it is ridiculed; next it is violently attacked; finally, it is held to be selfevident."  Schopenhauer

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 dozenforadime 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. 

Having no unique or profound knowledge of rifles, politics, women, or children, I had to come up with something.
Posting Peculiar PlusOnes since 13:30:15 7/1/04 
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 


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. 

I want to put methamphetamine vending machines in every school cafeteria.
 AR15fan 
anyone



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 


Might get some beeter help by posting this on the math and science section on preban, www.preban.com/forums/index.php?s=610309d4ce5849844dba661de76e6f21&showforum=41 It doesnt look very active over there though.



Team Member residing in occupied Californistan
CA, USA

My answer would be 42.
This is a great thread topic. btt 

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.



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)? 


I'm going to send a copy to some Russian masters of math in Siberia and see what they come up with...



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. 


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. . . . 


The cure? Go shooting, you'll feel much better!
USA

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! 
Resident therapist.
"Guns dont kill people, physics kill people."Anonymous quote from the 'net. 
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. 

C makes it easy to shoot yourself in the foot.
C++ makes it harder but if you do it blows away your whole leg. 
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