## SamIam 5 years ago Is there some special method to find the inverse of an elementary matrix?

1. SAMIAM

haha u r here without a notification

2. anonymous

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

i think they are looking for something using elementary row operations

4. SAMIAM

I mean elentary matrices

5. anonymous

I don't know what you mean by an elementary matrix.

6. SAMIAM

LOL neither do I ok i will read some more and try to figure oout

7. anonymous

Oh oh oh nevermind, sorry, my fault. You only need one row operation to change an elementary matrix into the identity.

8. SAMIAM

ok

9. anonymous

An example might be $\left[\begin{matrix}1 & 0 \\0 & 2\end{matrix}\right]$

10. SAMIAM

so the second row must be multiplied by a 1/2

11. anonymous
12. anonymous

So yes that's right samlam

13. SAMIAM

ya but like I am trying to find the inverse of this

14. SAMIAM

using products of elementary matrices

15. anonymous

That's easy to do, just use the usual technique of finding inverse.

16. anonymous

How about $\left[\begin{matrix}1 & 0 \\0 & 1/2\end{matrix}\right]$ ?

17. anonymous

If A is an elementary square matrix.

18. SAMIAM

y did we just do that?

19. SAMIAM

ohhhh cuz we are going backwards?

20. anonymous

Now write $$A= I_n A$$

21. SAMIAM

Not getting this stuff at all

22. anonymous

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

Now we can write $$A^{-1}=B$$

24. SAMIAM

ok so show sth an example plz

25. anonymous

I am too tired for a Latex example now :(

26. SAMIAM

LOL Oh u r so annoying

27. anonymous

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

ok

29. anonymous

That's an nice example Jemurray.

30. SAMIAM

lol

31. SAMIAM

*a

32. SAMIAM

A new day will bring fresh wisdom :D I think I gotta sleep over it

33. SAMIAM

FOOOOOOLLLLLLLL

34. anonymous

Yesssssssss :D

35. SAMIAM

LOL

36. SAMIAM

U kept on writing things and then deleting LOL

37. anonymous

I am evolving :P

38. SAMIAM

LOL I guess me too

39. anonymous

Now you believe in evolution? :P

40. SAMIAM

LOL uhhhh no! Did u see what i answered tanusingh

41. SAMIAM

in math chat

42. anonymous

no i didn't

43. SAMIAM

so go check lol

44. anonymous

lol

45. SAMIAM

Y did it take u so long to like say something to me

46. anonymous

Obviously I am evolving very slowly :P

47. SAMIAM

U knew it was me the whole time right?

48. anonymous

lol, Who me? :P

49. SAMIAM

ya

50. SAMIAM

lol me isnt samiam lol

51. anonymous

lol then who are you? :P

52. SAMIAM

idk u tell me

53. anonymous

How am I suppose to know? lol

54. SAMIAM

idk

55. SAMIAM

u know dont be stupid

56. anonymous

I am a fool NotStupid :D

57. SAMIAM

lol

58. SAMIAM

LOL me too

59. SAMIAM

y r u deleting all ur posts?

60. anonymous

haha you like her ? :P

61. SAMIAM

I love her

62. anonymous

I don't want others to know ;)

63. SAMIAM

LOL

64. anonymous

and I love her too lol :D

65. SAMIAM

star told ever1 that i am rld lol

66. SAMIAM

no i love her more

67. anonymous

star told ever1 ?

68. SAMIAM

ys she was mad at me

69. anonymous

who is star and ever1?

70. SAMIAM

star is a girl and everyone LOL

71. SAMIAM

whtvr she was mad that i asked her out and pretended to be a guy LOL

72. SAMIAM

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

FOOOOLLLLL I figured out what to do LOL

74. anonymous

u have digressed frm d topic