SamIam
  • SamIam
Is there some special method to find the inverse of an elementary matrix?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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SamIam
  • SamIam
haha u r here without a notification
anonymous
  • 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 \[\frac{1}{ad-bc} \left[\begin{matrix}d & -b\\ -c &a\end{matrix}\right]\]
SamIam
  • SamIam
i think they are looking for something using elementary row operations

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SamIam
  • SamIam
I mean elentary matrices
anonymous
  • anonymous
I don't know what you mean by an elementary matrix.
SamIam
  • SamIam
LOL neither do I ok i will read some more and try to figure oout
anonymous
  • anonymous
Oh oh oh nevermind, sorry, my fault. You only need one row operation to change an elementary matrix into the identity.
SamIam
  • SamIam
ok
anonymous
  • anonymous
An example might be \[\left[\begin{matrix}1 & 0 \\0 & 2\end{matrix}\right]\]
SamIam
  • SamIam
so the second row must be multiplied by a 1/2
anonymous
  • anonymous
http://en.wikipedia.org/wiki/Elementary_matrix
anonymous
  • anonymous
So yes that's right samlam
SamIam
  • SamIam
ya but like I am trying to find the inverse of this
SamIam
  • SamIam
using products of elementary matrices
anonymous
  • anonymous
That's easy to do, just use the usual technique of finding inverse.
anonymous
  • anonymous
How about \[\left[\begin{matrix}1 & 0 \\0 & 1/2\end{matrix}\right]\] ?
anonymous
  • anonymous
If A is an elementary square matrix.
SamIam
  • SamIam
y did we just do that?
SamIam
  • SamIam
ohhhh cuz we are going backwards?
anonymous
  • anonymous
Now write \( A= I_n A \)
SamIam
  • SamIam
Not getting this stuff at all
anonymous
  • 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.
anonymous
  • anonymous
Now we can write \( A^{-1}=B \)
SamIam
  • SamIam
ok so show sth an example plz
anonymous
  • anonymous
I am too tired for a Latex example now :(
SamIam
  • SamIam
LOL Oh u r so annoying
anonymous
  • 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.
SamIam
  • SamIam
ok
anonymous
  • anonymous
That's an nice example Jemurray.
SamIam
  • SamIam
lol
SamIam
  • SamIam
*a
SamIam
  • SamIam
A new day will bring fresh wisdom :D I think I gotta sleep over it
SamIam
  • SamIam
FOOOOOOLLLLLLLL
anonymous
  • anonymous
Yesssssssss :D
SamIam
  • SamIam
LOL
SamIam
  • SamIam
U kept on writing things and then deleting LOL
anonymous
  • anonymous
I am evolving :P
SamIam
  • SamIam
LOL I guess me too
anonymous
  • anonymous
Now you believe in evolution? :P
SamIam
  • SamIam
LOL uhhhh no! Did u see what i answered tanusingh
SamIam
  • SamIam
in math chat
anonymous
  • anonymous
no i didn't
SamIam
  • SamIam
so go check lol
anonymous
  • anonymous
lol
SamIam
  • SamIam
Y did it take u so long to like say something to me
anonymous
  • anonymous
Obviously I am evolving very slowly :P
SamIam
  • SamIam
U knew it was me the whole time right?
anonymous
  • anonymous
lol, Who me? :P
SamIam
  • SamIam
ya
SamIam
  • SamIam
lol me isnt samiam lol
anonymous
  • anonymous
lol then who are you? :P
SamIam
  • SamIam
idk u tell me
anonymous
  • anonymous
How am I suppose to know? lol
SamIam
  • SamIam
idk
SamIam
  • SamIam
u know dont be stupid
anonymous
  • anonymous
I am a fool NotStupid :D
SamIam
  • SamIam
lol
SamIam
  • SamIam
LOL me too
SamIam
  • SamIam
y r u deleting all ur posts?
anonymous
  • anonymous
haha you like her ? :P
SamIam
  • SamIam
I love her
anonymous
  • anonymous
I don't want others to know ;)
SamIam
  • SamIam
LOL
anonymous
  • anonymous
and I love her too lol :D
SamIam
  • SamIam
star told ever1 that i am rld lol
SamIam
  • SamIam
no i love her more
anonymous
  • anonymous
star told ever1 ?
SamIam
  • SamIam
ys she was mad at me
anonymous
  • anonymous
who is star and ever1?
SamIam
  • SamIam
star is a girl and everyone LOL
SamIam
  • SamIam
whtvr she was mad that i asked her out and pretended to be a guy LOL
SamIam
  • 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
SamIam
  • SamIam
FOOOOLLLLL I figured out what to do LOL
anonymous
  • anonymous
u have digressed frm d topic

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