@Bahrom

- angela210793

@Bahrom

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- angela210793

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- bahrom7893

just so u know i sucked at linear algebra, no idea how i got an A lol

- angela210793

tht means u didn't....:P tht means ur talented :P

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## More answers

- bahrom7893

Oh it's that matrix multiplied n times...

- bahrom7893

hold on.. let me see if i can find anything

- bahrom7893

im trying to do this for general case... a,b,c,d

- anonymous

too bad only bahrom can help

- angela210793

ok..take ur time ^^

- angela210793

@Everyone if u want to help...feel free to do it

- anonymous

if n = odd it is the same matrix and if n = even it is the diagonal matrix

- phi

don't you diagonalize the matrix into A=SDS^(-1)
and then A^n= S D^n S^-1

- anonymous

i meant identity matrix (no just diagonal)

- angela210793

@Saiberz why is it the same??? for n=2 i got
1 0
0 1
@Phi wht is SDS??? O.o

- anonymous

then even = matrix
and odd = same

- anonymous

*ident matrix

- nenadmatematika

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- phi

eigenvectors and eigenvalues. You did not get that far. But this is a special case
saiberz has the answer

- bahrom7893

wait this is eigenvectors?

- phi

you alternate between A and I

- angela210793

wht is/are eigenvectors????????? O.o

- nenadmatematika

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- bahrom7893

lol good question, my prof never managed to cover that

- angela210793

@Nenad i don't get it at all :S

- bahrom7893

he's row reducing the matrix

- bahrom7893

nenand, can you do that in here and still have the same answer?

- nenadmatematika

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- 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

what's T?

- 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

@nenad where did lambda come from ?

- 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

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

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

angela is this from a textbook?

- angela210793

wht r these famous eigenvectors..this is the first time i've heard these...

- 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

my home-works :((((

- 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

I would like to know what are Eigenvectors & Eigenvalues ?

- 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

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

page no.16 :P

- nenadmatematika

hahaha :D

- bahrom7893

OHHH phi LOL!

- bahrom7893

i feel stupid.. -_-

- bahrom7893

i should've just tried to multiply this actual product, not the freakin general abcd case..

- angela210793

ok how abt
|dw:1329491265305:dw|

- bahrom7893

that's also identity.. i think cuz u'll get Cos^2 and Sin^2..

- phi

if you know your trig identities
A*A gets you
[ cos 2x -sin2x ]
[ sin 2x cos 2x ]

- angela210793

oh yes i know...i had multiplied -sinx with cosx instead of sinx...
thanks :)

- 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

:O:O OMG!!! Can i have ur brain just for one semester pleaseeeee :(((((((

- anonymous

Lol angela

- bahrom7893

lol phi wanna swap brains? well actually i want to keep mine hahaha, though u are better than me at math..

- 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

hahaha lol yea.. i feel the same way when it comes to certain problems lol

- angela210793

xD

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