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LOOSEr

  • 2 years ago

what is a 3x3 invertible matrix?

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  1. tkhunny
    • 2 years ago
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    Are you OK with what a 3x3 matrix is?

  2. mathsmind
    • 2 years ago
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    do you want a formal definition or a solved example showing all steps of inverting a 3x3 matrix?

  3. LOOSEr
    • 2 years ago
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    a solved example would be great

  4. mathsmind
    • 2 years ago
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    ok

  5. LOOSEr
    • 2 years ago
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    @mathsmind ???

  6. LOOSEr
    • 2 years ago
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    which means its determinant cant be 0?

  7. mathsmind
    • 2 years ago
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    yest i will show you the full steps

  8. mathsmind
    • 2 years ago
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    consider the following matrix

  9. LOOSEr
    • 2 years ago
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    PLZ continue

  10. mathsmind
    • 2 years ago
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    \[A=\left[\begin{matrix}1 & -2 & 0\\ 3& 1 & 5\\ -1 & 2 & 3\end{matrix}\right]\]

  11. mathsmind
    • 2 years ago
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    Step one: \[A^T\]

  12. mathsmind
    • 2 years ago
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    which means transpose of rows and columns of A

  13. mathsmind
    • 2 years ago
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    \[A^T=\left[\begin{matrix}1 & 3 & -1\\ -2& 1 & 2\\ 0 & 5 & 3\end{matrix}\right]\]

  14. mathsmind
    • 2 years ago
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    Step Two: find the adjoint or adjugate of A, which implies that we replace each element by their cofactor...

  15. LOOSEr
    • 2 years ago
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    If P = \begin{bmatrix} a &b &c \\ d &e &f \\ g &h &i \end{bmatrix}

  16. mathsmind
    • 2 years ago
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    now please concentrate on this step it is simple but requires a bit of accuracy

  17. LOOSEr
    • 2 years ago
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    And P^4=2P how can we find P

  18. mathsmind
    • 2 years ago
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    let's finish this first part then i will come to the 2nd question, you asked me first for a numerical example

  19. mathsmind
    • 2 years ago
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    so we need to find adjA

  20. LOOSEr
    • 2 years ago
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    I know how to find a inverse matrix. So, can u plz do the 2nd question

  21. mathsmind
    • 2 years ago
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    ok sure

  22. LOOSEr
    • 2 years ago
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    any idea?

  23. mathsmind
    • 2 years ago
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    yes sorry am on the phone, but just a quick hint for P^n we use the principle of induction

  24. mathsmind
    • 2 years ago
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    i will show you shortly

  25. LOOSEr
    • 2 years ago
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    @mathsmind ???

  26. LOOSEr
    • 2 years ago
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    @mathsmind why is taking so long?

  27. mathsmind
    • 2 years ago
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    sorry back, am at work

  28. mathsmind
    • 2 years ago
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    now P^4 means you are multiplying your matrix by itself 4 times.

  29. LOOSEr
    • 2 years ago
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    yep

  30. mathsmind
    • 2 years ago
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    you know how to multiply the, it would be PP=P^2, then P^2P=P^3. then P^3P=P^4

  31. LOOSEr
    • 2 years ago
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    But it would be really long

  32. mathsmind
    • 2 years ago
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    well this is the world of Matrices...

  33. mathsmind
    • 2 years ago
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    are you thinking of algebraic operation on matrices such as taking the inverse of 2P

  34. mathsmind
    • 2 years ago
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    or subtracting p^4-2P=0 in order to find the new P?

  35. LOOSEr
    • 2 years ago
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    Isn't there any short way

  36. mathsmind
    • 2 years ago
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    have you done hermitian matrices...

  37. LOOSEr
    • 2 years ago
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    nope

  38. mathsmind
    • 2 years ago
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    listen can we kindly finish this tonight because it is 5 am and i need to go ...

  39. LOOSEr
    • 2 years ago
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    okay

  40. mathsmind
    • 2 years ago
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    i will provide you with full solution even if you are not online ok

  41. mathsmind
    • 2 years ago
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    see ya tonight

  42. LOOSEr
    • 2 years ago
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    @ParthKohli

  43. Hero
    • 2 years ago
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    lol, you still here? I thought you got help

  44. LOOSEr
    • 2 years ago
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    No

  45. LOOSEr
    • 2 years ago
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    can u do it?

  46. LOOSEr
    • 2 years ago
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    Short way

  47. ParthKohli
    • 2 years ago
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    I haven't done matrices yet: I am stuck with number theory at the moment.

  48. ParthKohli
    • 2 years ago
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    Nope.

  49. yummydum
    • 2 years ago
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    http://www.wikihow.com/Inverse-a-3X3-Matrix

  50. sauravshakya
    • 2 years ago
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    @looser there are many matrices such that P^4=2P but only one is invertible which is |dw:1361026643638:dw|

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