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[NEED HELP !] Linear Systems Calculations

  1. Jun 27, 2011 #1
    Hi guys/gals,

    First post here - in need of some desperate last minute help. Today is my last day to study and I will have my final exam tommorow. I've been doing past papers all day, and there a few questions I have no idea/never seen before in my course material.

    x59nqu.jpg
    Part (c) I have no idea what to do. I know I need to convert the 4sqrt2 into Cartesian, but I have no idea how...

    Part (d) I'm very close to getting, but I end up getting -cos^2(theta) + (-1) sin^2(theta) = 0

    Part (e) is related to part (d), so I'm not too sure at the moment.

    n5skg1.jpg
    I know that there is the rule that when there is a matrix A, A1v1=A2v2. However, these eigenvalues are imaginary, so how do I calculate the eigenvectors?

    ffbywg.jpg
    In a)i) of this question, I calculated -1/2 and -1 as the values of M (i.e. when you let Un=kM^n). I just want to double check these are correct, and also would like somebody to guide me in part ii). I have no idea how to calculate this using the results of part i)


    MANY MANY MANY thanks to whoever is able to help me out here. I think I may have already failed 1 subject this semster, and do not want to make it 2.

    Cheers,

    EDIT- extremely sorry for the image size, I don't know how to re-frame it. it's a photo from my phone haha
     
  2. jcsd
  3. Jun 27, 2011 #2

    rock.freak667

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    Homework Helper

    For the resizing thing, if you upload to imageshack there is an option for it.

    First image:

    c)the 4√2 is just a constant, so when you put eiπ/4 into cartesian form, you would multiply it by 4√2.

    d) If you consider z1z2 in polar form you will get r2 right? So just expand z1z2 in cartesian form and then put that equal to r2 [z1 is the z in the question and z2 is its conjugate]

    e) Well you want to find sin5θ, so consider expanding (cosθ+isinθ)5 (which is equak to cos5θ+isin5θ by De Moivre's theorem) and equate real and imaginary parts.

    I am not too well versed on the topics in the second and third images, so I can't really help you there.
     
    Last edited: Jun 27, 2011
  4. Jun 28, 2011 #3
    Thanks for the response. I think I get it a little better now.

    Any takers for 2nd+3rd image?
     
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