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

- SamIam

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

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- katieb

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- SamIam

haha u r here without a notification

- 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

i think they are looking for something using elementary row operations

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- SamIam

I mean elentary matrices

- anonymous

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

- SamIam

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

- anonymous

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

- SamIam

ok

- anonymous

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

- SamIam

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

- anonymous

http://en.wikipedia.org/wiki/Elementary_matrix

- anonymous

So yes that's right samlam

- SamIam

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

- SamIam

using products of elementary matrices

- anonymous

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

- anonymous

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

- anonymous

If A is an elementary square matrix.

- SamIam

y did we just do that?

- SamIam

ohhhh cuz we are going backwards?

- anonymous

Now write \( A= I_n A \)

- SamIam

Not getting this stuff at all

- 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

Now we can write \( A^{-1}=B \)

- SamIam

ok so show sth an example plz

- anonymous

I am too tired for a Latex example now :(

- SamIam

LOL Oh u r so annoying

- 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

ok

- anonymous

That's an nice example Jemurray.

- SamIam

lol

- SamIam

*a

- SamIam

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

- SamIam

FOOOOOOLLLLLLLL

- anonymous

Yesssssssss :D

- SamIam

LOL

- SamIam

U kept on writing things and then deleting LOL

- anonymous

I am evolving :P

- SamIam

LOL I guess me too

- anonymous

Now you believe in evolution? :P

- SamIam

LOL uhhhh no!
Did u see what i answered tanusingh

- SamIam

in math chat

- anonymous

no i didn't

- SamIam

so go check lol

- anonymous

lol

- SamIam

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

- anonymous

Obviously I am evolving very slowly :P

- SamIam

U knew it was me the whole time right?

- anonymous

lol, Who me? :P

- SamIam

ya

- SamIam

lol me isnt samiam lol

- anonymous

lol then who are you? :P

- SamIam

idk u tell me

- anonymous

How am I suppose to know? lol

- SamIam

idk

- SamIam

u know dont be stupid

- anonymous

I am a fool NotStupid :D

- SamIam

lol

- SamIam

LOL me too

- SamIam

y r u deleting all ur posts?

- anonymous

haha you like her ? :P

- SamIam

I love her

- anonymous

I don't want others to know ;)

- SamIam

LOL

- anonymous

and I love her too lol :D

- SamIam

star told ever1 that i am rld lol

- SamIam

no i love her more

- anonymous

star told ever1 ?

- SamIam

ys she was mad at me

- anonymous

who is star and ever1?

- SamIam

star is a girl and everyone LOL

- SamIam

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

- 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

FOOOOLLLLL I figured out what to do LOL

- anonymous

u have digressed frm d topic

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