angela210793
  • angela210793
@Bahrom
Mathematics
  • Stacey Warren - Expert brainly.com
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jamiebookeater
  • jamiebookeater
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angela210793
  • angela210793
|dw:1329489110068:dw|
bahrom7893
  • bahrom7893
just so u know i sucked at linear algebra, no idea how i got an A lol
angela210793
  • angela210793
tht means u didn't....:P tht means ur talented :P

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bahrom7893
  • bahrom7893
Oh it's that matrix multiplied n times...
bahrom7893
  • bahrom7893
hold on.. let me see if i can find anything
bahrom7893
  • bahrom7893
im trying to do this for general case... a,b,c,d
anonymous
  • anonymous
too bad only bahrom can help
angela210793
  • angela210793
ok..take ur time ^^
angela210793
  • angela210793
@Everyone if u want to help...feel free to do it
anonymous
  • anonymous
if n = odd it is the same matrix and if n = even it is the diagonal matrix
phi
  • phi
don't you diagonalize the matrix into A=SDS^(-1) and then A^n= S D^n S^-1
anonymous
  • anonymous
i meant identity matrix (no just diagonal)
angela210793
  • angela210793
@Saiberz why is it the same??? for n=2 i got 1 0 0 1 @Phi wht is SDS??? O.o
anonymous
  • anonymous
then even = matrix and odd = same
anonymous
  • anonymous
*ident matrix
nenadmatematika
  • nenadmatematika
|dw:1329490024595:dw|
phi
  • phi
eigenvectors and eigenvalues. You did not get that far. But this is a special case saiberz has the answer
bahrom7893
  • bahrom7893
wait this is eigenvectors?
phi
  • phi
you alternate between A and I
angela210793
  • angela210793
wht is/are eigenvectors????????? O.o
nenadmatematika
  • nenadmatematika
|dw:1329490292192:dw|
bahrom7893
  • bahrom7893
lol good question, my prof never managed to cover that
angela210793
  • angela210793
@Nenad i don't get it at all :S
bahrom7893
  • bahrom7893
he's row reducing the matrix
bahrom7893
  • bahrom7893
nenand, can you do that in here and still have the same answer?
nenadmatematika
  • nenadmatematika
|dw:1329490445758:dw|
nenadmatematika
  • nenadmatematika
now do the inverse of T, and multiply these matrices and you'll get A^n....if you'd like to check the result plug in n=1 and you'll get A^1=A...the matrix you started with :D this is the basic method for finding A^n using eigenvalues and vectors...:D
bahrom7893
  • bahrom7893
what's T?
bahrom7893
  • bahrom7893
ohh well, sorry angela, i got to like n=3, it looks crazy and we never even covered eigenvalues and eigenvectors (told ya i sucked at lin algebra)
anonymous
  • anonymous
@nenad where did lambda come from ?
angela210793
  • angela210793
@Nenad ur making me feel soooooo stupid :S i'm not getting it at all @Bahrom nvm :) thnx for trying :))))))))) Thank you everyone :-)))
nenadmatematika
  • nenadmatematika
I don't know how can I explain it to you like this....I don't know any other way except using this method :(
bahrom7893
  • bahrom7893
nenand eigenvectors are covered all the way at the end of lin algebra... we didnt even get there. Let's think about this more.. maybe theres a shortcut
bahrom7893
  • bahrom7893
angela is this from a textbook?
angela210793
  • angela210793
wht r these famous eigenvectors..this is the first time i've heard these...
nenadmatematika
  • nenadmatematika
well we used to this at my faculty with matrices 3 times 3, and I think we didn't use any other method....
angela210793
  • angela210793
my home-works :((((
bahrom7893
  • bahrom7893
well is the hw from some textbook? If it is, post the author, title, edition, and the page# and number of the problem
anonymous
  • anonymous
I would like to know what are Eigenvectors & Eigenvalues ?
angela210793
  • angela210793
do u know albanian Bahrom???? tht would be great title:''matematika per fakultetin e ekonomise,algjebra lineare dhe analiza matematike'' authors:''Thoma Mitre,Omer stringa,bashkim ruseti'' :P
phi
  • phi
This problem is just a special case. They want you to multiply it A*A to find you get I (identity). Then multiply again A*A*A= I*A= A, to get A, then multiply again A*A*A*A= I*I=I, and so on answer: n even I n odd A
angela210793
  • angela210793
page no.16 :P
nenadmatematika
  • nenadmatematika
hahaha :D
bahrom7893
  • bahrom7893
OHHH phi LOL!
bahrom7893
  • bahrom7893
i feel stupid.. -_-
bahrom7893
  • bahrom7893
i should've just tried to multiply this actual product, not the freakin general abcd case..
angela210793
  • angela210793
ok how abt |dw:1329491265305:dw|
bahrom7893
  • bahrom7893
that's also identity.. i think cuz u'll get Cos^2 and Sin^2..
phi
  • phi
if you know your trig identities A*A gets you [ cos 2x -sin2x ] [ sin 2x cos 2x ]
angela210793
  • angela210793
oh yes i know...i had multiplied -sinx with cosx instead of sinx... thanks :)
phi
  • phi
to keep going we need to use cos(A+B)= cosA cosB - sinA sinB where A= n*x and B= x this allows us to find cos( (n+1)x)= cos(nx) cos(x) - sin(nx)sin(x) also sin(A+B)= sinA cosB + sinB cosA so sin ( (n+1)x)= sin(nx) cos(x) + sin(x) cos(nx)
angela210793
  • angela210793
:O:O OMG!!! Can i have ur brain just for one semester pleaseeeee :(((((((
anonymous
  • anonymous
Lol angela
bahrom7893
  • bahrom7893
lol phi wanna swap brains? well actually i want to keep mine hahaha, though u are better than me at math..
angela210793
  • angela210793
i love my brain cause i got so much information in there....but when it comes to math....it doesn't work :P
bahrom7893
  • bahrom7893
hahaha lol yea.. i feel the same way when it comes to certain problems lol
angela210793
  • angela210793
xD

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