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angela210793

  • 3 years ago

@Bahrom

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  1. angela210793
    • 3 years ago
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    |dw:1329489110068:dw|

  2. bahrom7893
    • 3 years ago
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    just so u know i sucked at linear algebra, no idea how i got an A lol

  3. angela210793
    • 3 years ago
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    tht means u didn't....:P tht means ur talented :P

  4. bahrom7893
    • 3 years ago
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    Oh it's that matrix multiplied n times...

  5. bahrom7893
    • 3 years ago
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    hold on.. let me see if i can find anything

  6. bahrom7893
    • 3 years ago
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    im trying to do this for general case... a,b,c,d

  7. Tomas.A
    • 3 years ago
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    too bad only bahrom can help

  8. angela210793
    • 3 years ago
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    ok..take ur time ^^

  9. angela210793
    • 3 years ago
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    @Everyone if u want to help...feel free to do it

  10. saiberz
    • 3 years ago
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    if n = odd it is the same matrix and if n = even it is the diagonal matrix

  11. phi
    • 3 years ago
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    don't you diagonalize the matrix into A=SDS^(-1) and then A^n= S D^n S^-1

  12. saiberz
    • 3 years ago
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    i meant identity matrix (no just diagonal)

  13. angela210793
    • 3 years ago
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    @Saiberz why is it the same??? for n=2 i got 1 0 0 1 @Phi wht is SDS??? O.o

  14. saiberz
    • 3 years ago
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    then even = matrix and odd = same

  15. saiberz
    • 3 years ago
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    *ident matrix

  16. nenadmatematika
    • 3 years ago
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    |dw:1329490024595:dw|

  17. phi
    • 3 years ago
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    eigenvectors and eigenvalues. You did not get that far. But this is a special case saiberz has the answer

  18. bahrom7893
    • 3 years ago
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    wait this is eigenvectors?

  19. phi
    • 3 years ago
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    you alternate between A and I

  20. angela210793
    • 3 years ago
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    wht is/are eigenvectors????????? O.o

  21. nenadmatematika
    • 3 years ago
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    |dw:1329490292192:dw|

  22. bahrom7893
    • 3 years ago
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    lol good question, my prof never managed to cover that

  23. angela210793
    • 3 years ago
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    @Nenad i don't get it at all :S

  24. bahrom7893
    • 3 years ago
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    he's row reducing the matrix

  25. bahrom7893
    • 3 years ago
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    nenand, can you do that in here and still have the same answer?

  26. nenadmatematika
    • 3 years ago
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    |dw:1329490445758:dw|

  27. nenadmatematika
    • 3 years ago
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    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

  28. bahrom7893
    • 3 years ago
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    what's T?

  29. bahrom7893
    • 3 years ago
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    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)

  30. StArAnGeL
    • 3 years ago
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    @nenad where did lambda come from ?

  31. angela210793
    • 3 years ago
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    @Nenad ur making me feel soooooo stupid :S i'm not getting it at all @Bahrom nvm :) thnx for trying :))))))))) Thank you everyone :-)))

  32. nenadmatematika
    • 3 years ago
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    I don't know how can I explain it to you like this....I don't know any other way except using this method :(

  33. bahrom7893
    • 3 years ago
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    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

  34. bahrom7893
    • 3 years ago
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    angela is this from a textbook?

  35. angela210793
    • 3 years ago
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    wht r these famous eigenvectors..this is the first time i've heard these...

  36. nenadmatematika
    • 3 years ago
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    well we used to this at my faculty with matrices 3 times 3, and I think we didn't use any other method....

  37. angela210793
    • 3 years ago
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    my home-works :((((

  38. bahrom7893
    • 3 years ago
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    well is the hw from some textbook? If it is, post the author, title, edition, and the page# and number of the problem

  39. StArAnGeL
    • 3 years ago
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    I would like to know what are Eigenvectors & Eigenvalues ?

  40. angela210793
    • 3 years ago
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    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

  41. phi
    • 3 years ago
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    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

  42. angela210793
    • 3 years ago
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    page no.16 :P

  43. nenadmatematika
    • 3 years ago
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    hahaha :D

  44. bahrom7893
    • 3 years ago
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    OHHH phi LOL!

  45. bahrom7893
    • 3 years ago
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    i feel stupid.. -_-

  46. bahrom7893
    • 3 years ago
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    i should've just tried to multiply this actual product, not the freakin general abcd case..

  47. angela210793
    • 3 years ago
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    ok how abt |dw:1329491265305:dw|

  48. bahrom7893
    • 3 years ago
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    that's also identity.. i think cuz u'll get Cos^2 and Sin^2..

  49. phi
    • 3 years ago
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    if you know your trig identities A*A gets you [ cos 2x -sin2x ] [ sin 2x cos 2x ]

  50. angela210793
    • 3 years ago
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    oh yes i know...i had multiplied -sinx with cosx instead of sinx... thanks :)

  51. phi
    • 3 years ago
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    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)

  52. angela210793
    • 3 years ago
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    :O:O OMG!!! Can i have ur brain just for one semester pleaseeeee :(((((((

  53. StArAnGeL
    • 3 years ago
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    Lol angela

  54. bahrom7893
    • 3 years ago
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    lol phi wanna swap brains? well actually i want to keep mine hahaha, though u are better than me at math..

  55. angela210793
    • 3 years ago
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    i love my brain cause i got so much information in there....but when it comes to math....it doesn't work :P

  56. bahrom7893
    • 3 years ago
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    hahaha lol yea.. i feel the same way when it comes to certain problems lol

  57. angela210793
    • 3 years ago
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    xD

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