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rishabh.mission

  • 2 years ago

matrix Question ....plz help

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  1. rishabh.mission
    • 2 years ago
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    See the attachment

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  2. rishabh.mission
    • 2 years ago
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    please just solve this Question

  3. phi
    • 2 years ago
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    one way is use the trig identities \[ \tan \left(\frac{x}{2} \right)= \frac{1-\cos\ x}{\sin\ x }=\frac{\sin\ x }{1+\cos\ x}\]

  4. rishabh.mission
    • 2 years ago
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    plz buddy solve this i don't have any idea how to solve..

  5. phi
    • 2 years ago
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    you could start by writing down I-A can you do that ?

  6. rishabh.mission
    • 2 years ago
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    yes i did

  7. rishabh.mission
    • 2 years ago
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    I have problem with that equation in the circle i shown.

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  8. phi
    • 2 years ago
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    call 2 sin^2(a/2) = x then it looks like 1-x+x

  9. phi
    • 2 years ago
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    **look at the top left expression. Doesn't that simplify?

  10. rishabh.mission
    • 2 years ago
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    :( not understand

  11. phi
    • 2 years ago
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    or are you asking how they got to that point ?

  12. rishabh.mission
    • 2 years ago
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    yes

  13. rishabh.mission
    • 2 years ago
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    :)

  14. rishabh.mission
    • 2 years ago
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    that's Eq^n 1st

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  15. phi
    • 2 years ago
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    you just posted the left side. on the right side (the messy one) they did I-A times the other matrix I take it you understand how they got to the matrix labeled (2) ?

  16. phi
    • 2 years ago
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    the matrix above the circled stuff....

  17. rishabh.mission
    • 2 years ago
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    hmm

  18. phi
    • 2 years ago
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    We could go through that mess, but I would replace tan(a/2) with (1-cos)/sin in the top left entry: cos a + sin a tan(a/2) becomes cos a + sin a * (1-cos a)/sina= cosa + 1 -cosa = 1 which is what we want. Doing the way you have laid out is messier, but we can go through that if you want

  19. rishabh.mission
    • 2 years ago
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    can we write \[\cos \alpha/2 = (1-\tan ^{2} \alpha/2) / (1+\tan^{2} \alpha/2)\]

  20. rishabh.mission
    • 2 years ago
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    sorry ** its \[\cos \alpha \]

  21. Hoa
    • 2 years ago
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    can I say something?

  22. rishabh.mission
    • 2 years ago
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    yes please .. @hoa

  23. Hoa
    • 2 years ago
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    left side, i got I+A = \[\left[\begin{matrix}1 & -\tan \frac{ \alpha }{ 2} \\ \tan \frac{ \alpha }{ 2 } & 1\end{matrix}\right]\] = right side = (I-A) [ ] = \[\left[\begin{matrix}1 & \tan \frac{ \alpha }{ 2}\\ -\tan \frac{ \alpha }{ 2 } & 1\end{matrix}\right]\left[\begin{matrix}\cos & -\sin \\ \sin & \cos\end{matrix}\right]\]

  24. Hoa
    • 2 years ago
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    i just do the first term:

  25. rishabh.mission
    • 2 years ago
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    that's correct i already done this

  26. Hoa
    • 2 years ago
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    a11= cos + tanalpha/2* sin= 1

  27. Hoa
    • 2 years ago
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    you can expand the term like what phi says and you get 1 exactly what the left side matrix is

  28. phi
    • 2 years ago
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    for the top right of (2 - sin a + cos a tan(a/2) factor out -tan(a/2) (because that will be the answer) -tan(a/2) ( sin(a)/ tan(a/2) - cos(a)) replace 1/tan(a/2) inside the parens by multiplying by (1+cos(a))/sin a we get -tan(a/2) ( sin(a)*(1+cosa)/sina - cos(a))= -tan(a/2) ( 1 +cosa -cos a)= -tan(a/2) do the same thing for the other entries.

  29. Hoa
    • 2 years ago
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    because \[\cos + \sin *\tan \frac{ \alpha }{ 2 }= \cos + \sin\frac{ \sin }{ 1+\cos }= \frac{ \cos +\cos^2 +\sin^2 }{ 1+\cos}\] =1

  30. Hoa
    • 2 years ago
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    bingo. phi!! I am with you now. @rishabh.mission is it right?

  31. rishabh.mission
    • 2 years ago
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    Just last Query ... how both that matrix same ?

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  32. Hoa
    • 2 years ago
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    why do you make that question, why do you separate (I-A) and [cos sin....] matrix to calculate just the latter like that.?you may mess them up.

  33. Hoa
    • 2 years ago
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    they are a block and calculate together.

  34. phi
    • 2 years ago
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    I will do the top left entry 1- tan^2(a/2) is 1- sin^2(a/2)/cos^2(a/2) putting over a common denominator we get (cos^2(a/2) - sin^2(a/2)/cos^2(a/2) the numerator is cos(a) (one of version of the identity you need to know or look up) the denominator of the tp left entry 1+ tan^2(a/2) is 1+ sin^2(a/2)/cos^2(a/2) = (cos^2(a/2) + sin^2(a/2)/cos^2(a/2) = 1/cos^(a/2) the cos^2(a/2) cancels and we are left with cos a

  35. phi
    • 2 years ago
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    Can you follow that?

  36. rishabh.mission
    • 2 years ago
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    ok i done

  37. rishabh.mission
    • 2 years ago
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    @phi i can also use this cos(2a)=1-tan^2a/1+tan^2a

  38. phi
    • 2 years ago
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    that identity is true, but I have not tried to use it to simplify you problem. I tried to explain how I would do you problem.

  39. rishabh.mission
    • 2 years ago
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    ok you can solve this using this identity

  40. phi
    • 2 years ago
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    It does not look like a fruitful way to proceed, as you have sin and cos

  41. rishabh.mission
    • 2 years ago
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    No we can do using that Eq too

  42. rishabh.mission
    • 2 years ago
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    i'll show it to you in morning :)

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