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    (Original post by HFancy1997)
    but the Eigenvector is divided by three so do you not divide it by 3 too?

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    no because a multiple of an eigenvector will still have the same corresponding eigenvalue.
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    (Original post by klosovic)
    no because a multiple of an eigenvector will still have the same corresponding eigenvalue.
    So it doesnt matter what multiple the eigenvector is, it still will always have the same eigenvalue? Didnt know thats

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    (Original post by HFancy1997)
    So it doesnt matter what multiple the eigenvector is, it still will always have the same eigenvalue? Didnt know thats

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    There isn't one specific eigenvector for each eigenvalue, so in that question they used two different eigenvectors which both work with the same eigenvalue.

    (1,-1,1/3) is the eigenvector they chose for the part you mentioned,
    so M^2 v = 2^2 v

    Just make sure the vector v is the same on both sides of the equation.
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    Could anyone help me on june 12 2bii, I got the real value for n, dont understand how they got the imaginary one

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    (Original post by HFancy1997)
    Could anyone help me on june 12 2bii, I got the real value for n, dont understand how they got the imaginary one

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    Since it must be imaginary it can't have any real component so therefore must lie on the imaginary axis. So the argument must be pi/2 + npi.

    Not sure if thats the best explanation but hope it helps.
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    (Original post by Bruhh)
    Since it must be imaginary it can't have any real component so therefore must lie on the imaginary axis. So the argument must be pi/2 + npi.

    Not sure if thats the best explanation but hope it helps.
    yeah it does thanks man

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    Anyone know how to do jan 13,2aii) ive never seen binomial used there?

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    (Original post by HFancy1997)
    Anyone know how to do jan 13,2aii) ive never seen binomial used there?

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    Get it into a bracket in the form (1+x)^n, so here it's (1+e^2jtheta)^n then use the previous part of the question to replace what's inside the bracket. There are a few other questions that use binomial in the same way.
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    (Original post by Alex621)
    Get it into a bracket in the form (1+x)^n, so here it's (1+e^2jtheta)^n then use the previous part of the question to replace what's inside the bracket. There are a few other questions that use binomial in the same way.
    what goes inside the bracket is it always (1+r)^n where r is the difference in terms?

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    (Original post by HFancy1997)
    what goes inside the bracket is it always (1+r)^n where r is the difference in terms?

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    That's how it's always been in past paper questions, I thought there were more but the only other 2 I could find were in Jan 07, and in the specimen A paper which I've attached in case you don't have it and wanted to have a look.

    I look at the binomial expansion formula in the booklet and try to compare it to 'C+jS' to work out what to put in the bracket. Sorry I can't explain it more clearly.
    Attached Images
  1. File Type: pdf A FP2.pdf (373.0 KB, 148 views)
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    June 13: 4 iv: any idea where they got the 1/2 from?
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    http://www.mei.org.uk/files/papers/J..._2013_June.pdf

    2aii)

    Does anybody understand their justification in the mark scheme for choosing ((5+root(5))/8)^0.5 instead of ((5-root(5))/8)^0.5 for the value of cos(18).

    It just says 'Cos(18) is closer to one', and I don't understand the logic behind this reasoning.
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    (Original post by Connorbwfc)
    http://www.mei.org.uk/files/papers/J..._2013_June.pdf

    2aii)

    Does anybody understand their justification in the mark scheme for choosing ((5+root(5))/8)^0.5 instead of ((5-root(5))/8)^0.5 for the value of cos(18).

    It just says 'Cos(18) is closer to one', and I don't understand the logic behind this reasoning.
    If you try arccos of both of them, the + one gives pi/10, whereas the - one give 3pi/10, so I assume only the first one is correct as pi/10 = 18 degrees, maybe? :lol: That question stumped me as well.
    I think what they're saying is cos(18) ≈ 1, so cos (theta) must be as large as possible, hence you choose the + as it gives a larger number.

    (Original post by Stallzy)
    June 13: 4 iv: any idea where they got the 1/2 from?
    I'm so confused by that as well, when you use by parts it just ends up looping round and I have no idea what you're supposed to do

    Edit: I think I just sorted it, if you write out the whole integration by parts formula, on the LHS you have the original integral, and on RHS you have the negative version of it, so add it onto the LHS, then you have 2(the original integral) so divide both sides by two, and then continue evaluating?
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    (Original post by HFancy1997)
    what goes inside the bracket is it always (1+r)^n where r is the difference in terms?

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    If you can't figure it out, often look back at earlier parts of the question, for example they asked you to express (1+e^(2jtheta)) in trig form already so in nearly all cases thats going to be used again further in the question.
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    (Original post by Alex621)
    If you try arccos of both of them, the + one gives pi/10, whereas the - one give 3pi/10, so I assume only the first one is correct as pi/10 = 18 degrees, maybe? :lol: That question stumped me as well.
    I think what they're saying is cos(18) ≈ 1, so cos (theta) must be as large as possible, hence you choose the + as it gives a larger number.



    I'm so confused by that as well, when you use by parts it just ends up looping round and I have no idea what you're supposed to do

    Edit: I think I just sorted it, if you write out the whole integration by parts formula, on the LHS you have the original integral, and on RHS you have the negative version of it, so add it onto the LHS, then you have 2(the original integral) so divide both sides by two, and then continue evaluating?
    Okay thanks. This kind of makes sense.
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    When you are writing down the diagonal matrix, do the eigenvalues have to be in increasing value going down the diagonal or can they be in any order?
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    http://www.mei.org.uk/files/papers/FP2_2014_June.pdf

    Please can someone explain the final answer for 4ii)

    I got an answer of 1/2 ln (2x/5 + root(4x^2/25 + 1)). I've subbed in values on my graphical calculator and it works, so i'm convinced that this is the correct answer.

    Please can someone explain why the answer in the mark scheme is completely different.
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    (Original post by groovy_q)
    When you are writing down the diagonal matrix, do the eigenvalues have to be in increasing value going down the diagonal or can they be in any order?
    They have to be in the same order as your eigenvectors in your P matrix. As long as the two are consistent then the order doesn't matter.
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    (Original post by Connorbwfc)
    http://www.mei.org.uk/files/papers/FP2_2014_June.pdf

    Please can someone explain the final answer for 4ii)

    I got an answer of 1/2 ln (2x/5 + root(4x^2/25 + 1)). I've subbed in values on my graphical calculator and it works, so i'm convinced that this is the correct answer.

    Please can someone explain why the answer in the mark scheme is completely different.
    Your answer is under the 'Guidance' section in the mark scheme.
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    (Original post by Alex621)
    Your answer is under the 'Guidance' section in the mark scheme.
    1/2 ln (2x/5 + root(4x^2/25 + 1) is my answer.

    The answer in the guidance section is ln (2x/5 + root(4x^2/25 + 1)

    Isn't this my answer without the 1/2 infront of it?
 
 
 
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