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just so u know i sucked at linear algebra, no idea how i got an A lol
tht means u didn't....:P tht means ur talented :P
Oh it's that matrix multiplied n times...
hold on.. let me see if i can find anything
im trying to do this for general case... a,b,c,d
too bad only bahrom can help
ok..take ur time ^^
if n = odd it is the same matrix and if n = even it is the diagonal matrix
don't you diagonalize the matrix into A=SDS^(-1) and then A^n= S D^n S^-1
i meant identity matrix (no just diagonal)
then even = matrix and odd = same
eigenvectors and eigenvalues. You did not get that far. But this is a special case saiberz has the answer
wait this is eigenvectors?
you alternate between A and I
wht is/are eigenvectors????????? O.o
lol good question, my prof never managed to cover that
he's row reducing the matrix
nenand, can you do that in here and still have the same answer?
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
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)
I don't know how can I explain it to you like this....I don't know any other way except using this method :(
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
angela is this from a textbook?
wht r these famous eigenvectors..this is the first time i've heard these...
well we used to this at my faculty with matrices 3 times 3, and I think we didn't use any other method....
my home-works :((((
well is the hw from some textbook? If it is, post the author, title, edition, and the page# and number of the problem
I would like to know what are Eigenvectors & Eigenvalues ?
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
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
page no.16 :P
OHHH phi LOL!
i feel stupid.. -_-
i should've just tried to multiply this actual product, not the freakin general abcd case..
ok how abt |dw:1329491265305:dw|
that's also identity.. i think cuz u'll get Cos^2 and Sin^2..
if you know your trig identities A*A gets you [ cos 2x -sin2x ] [ sin 2x cos 2x ]
oh yes i know...i had multiplied -sinx with cosx instead of sinx... thanks :)
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)
:O:O OMG!!! Can i have ur brain just for one semester pleaseeeee :(((((((
lol phi wanna swap brains? well actually i want to keep mine hahaha, though u are better than me at math..
i love my brain cause i got so much information in there....but when it comes to math....it doesn't work :P
hahaha lol yea.. i feel the same way when it comes to certain problems lol