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SamIam

  • 5 years ago

Is there some special method to find the inverse of an elementary matrix?

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  1. SAMIAM
    • 5 years ago
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    haha u r here without a notification

  2. anonymous
    • 5 years ago
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    Gaussian Row-Reduction is useful. For a two by two matrix, \[A =\left[\begin{matrix}a & b \\ c & d\end{matrix}\right]\] The inverse matrix is \[\frac{1}{ad-bc} \left[\begin{matrix}d & -b\\ -c &a\end{matrix}\right]\]

  3. SAMIAM
    • 5 years ago
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    i think they are looking for something using elementary row operations

  4. SAMIAM
    • 5 years ago
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    I mean elentary matrices

  5. anonymous
    • 5 years ago
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    I don't know what you mean by an elementary matrix.

  6. SAMIAM
    • 5 years ago
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    LOL neither do I ok i will read some more and try to figure oout

  7. anonymous
    • 5 years ago
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    Oh oh oh nevermind, sorry, my fault. You only need one row operation to change an elementary matrix into the identity.

  8. SAMIAM
    • 5 years ago
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    ok

  9. anonymous
    • 5 years ago
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    An example might be \[\left[\begin{matrix}1 & 0 \\0 & 2\end{matrix}\right]\]

  10. SAMIAM
    • 5 years ago
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    so the second row must be multiplied by a 1/2

  11. anonymous
    • 5 years ago
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    http://en.wikipedia.org/wiki/Elementary_matrix

  12. anonymous
    • 5 years ago
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    So yes that's right samlam

  13. SAMIAM
    • 5 years ago
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    ya but like I am trying to find the inverse of this

  14. SAMIAM
    • 5 years ago
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    using products of elementary matrices

  15. anonymous
    • 5 years ago
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    That's easy to do, just use the usual technique of finding inverse.

  16. anonymous
    • 5 years ago
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    How about \[\left[\begin{matrix}1 & 0 \\0 & 1/2\end{matrix}\right]\] ?

  17. anonymous
    • 5 years ago
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    If A is an elementary square matrix.

  18. SAMIAM
    • 5 years ago
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    y did we just do that?

  19. SAMIAM
    • 5 years ago
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    ohhhh cuz we are going backwards?

  20. anonymous
    • 5 years ago
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    Now write \( A= I_n A \)

  21. SAMIAM
    • 5 years ago
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    Not getting this stuff at all

  22. anonymous
    • 5 years ago
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    Then do sequence of row operation on the L.H.S and the prefactor I_n till we obtain \( I_n=BA \) This step will be easy since A is an elementary matrix.

  23. anonymous
    • 5 years ago
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    Now we can write \( A^{-1}=B \)

  24. SAMIAM
    • 5 years ago
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    ok so show sth an example plz

  25. anonymous
    • 5 years ago
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    I am too tired for a Latex example now :(

  26. SAMIAM
    • 5 years ago
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    LOL Oh u r so annoying

  27. anonymous
    • 5 years ago
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    http://nptel.iitm.ac.in/courses/Webcourse-contents/IIT-KANPUR/mathematics-2/node27.html That's row-reduction. The only difference between that and what you're talking about with elementary matrices is that when the matrices are elementary its far easier.

  28. SAMIAM
    • 5 years ago
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    ok

  29. anonymous
    • 5 years ago
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    That's an nice example Jemurray.

  30. SAMIAM
    • 5 years ago
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    lol

  31. SAMIAM
    • 5 years ago
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    *a

  32. SAMIAM
    • 5 years ago
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    A new day will bring fresh wisdom :D I think I gotta sleep over it

  33. SAMIAM
    • 5 years ago
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    FOOOOOOLLLLLLLL

  34. anonymous
    • 5 years ago
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    Yesssssssss :D

  35. SAMIAM
    • 5 years ago
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    LOL

  36. SAMIAM
    • 5 years ago
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    U kept on writing things and then deleting LOL

  37. anonymous
    • 5 years ago
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    I am evolving :P

  38. SAMIAM
    • 5 years ago
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    LOL I guess me too

  39. anonymous
    • 5 years ago
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    Now you believe in evolution? :P

  40. SAMIAM
    • 5 years ago
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    LOL uhhhh no! Did u see what i answered tanusingh

  41. SAMIAM
    • 5 years ago
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    in math chat

  42. anonymous
    • 5 years ago
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    no i didn't

  43. SAMIAM
    • 5 years ago
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    so go check lol

  44. anonymous
    • 5 years ago
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    lol

  45. SAMIAM
    • 5 years ago
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    Y did it take u so long to like say something to me

  46. anonymous
    • 5 years ago
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    Obviously I am evolving very slowly :P

  47. SAMIAM
    • 5 years ago
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    U knew it was me the whole time right?

  48. anonymous
    • 5 years ago
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    lol, Who me? :P

  49. SAMIAM
    • 5 years ago
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    ya

  50. SAMIAM
    • 5 years ago
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    lol me isnt samiam lol

  51. anonymous
    • 5 years ago
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    lol then who are you? :P

  52. SAMIAM
    • 5 years ago
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    idk u tell me

  53. anonymous
    • 5 years ago
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    How am I suppose to know? lol

  54. SAMIAM
    • 5 years ago
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    idk

  55. SAMIAM
    • 5 years ago
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    u know dont be stupid

  56. anonymous
    • 5 years ago
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    I am a fool NotStupid :D

  57. SAMIAM
    • 5 years ago
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    lol

  58. SAMIAM
    • 5 years ago
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    LOL me too

  59. SAMIAM
    • 5 years ago
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    y r u deleting all ur posts?

  60. anonymous
    • 5 years ago
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    haha you like her ? :P

  61. SAMIAM
    • 5 years ago
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    I love her

  62. anonymous
    • 5 years ago
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    I don't want others to know ;)

  63. SAMIAM
    • 5 years ago
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    LOL

  64. anonymous
    • 5 years ago
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    and I love her too lol :D

  65. SAMIAM
    • 5 years ago
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    star told ever1 that i am rld lol

  66. SAMIAM
    • 5 years ago
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    no i love her more

  67. anonymous
    • 5 years ago
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    star told ever1 ?

  68. SAMIAM
    • 5 years ago
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    ys she was mad at me

  69. anonymous
    • 5 years ago
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    who is star and ever1?

  70. SAMIAM
    • 5 years ago
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    star is a girl and everyone LOL

  71. SAMIAM
    • 5 years ago
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    whtvr she was mad that i asked her out and pretended to be a guy LOL

  72. SAMIAM
    • 5 years ago
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    Every1 in that group knew that I waas rld but her and so i played a lil joke on her but she like started calling me names and whtvr

  73. SAMIAM
    • 5 years ago
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    FOOOOLLLLL I figured out what to do LOL

  74. anonymous
    • 5 years ago
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    u have digressed frm d topic

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