Question

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

Answer 1

haha u r here without a notification

Answer 2

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
\[\frac{1}{ad-bc} \left[\begin{matrix}d & -b\\ -c &a\end{matrix}\right]\]

Answer 3

i think they are looking for something using elementary row operations

Answer 4

I mean elentary matrices

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

ok

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

So yes that's right samlam

Answer 13

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

Answer 14

using products of elementary matrices

Answer 15

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

Answer 16

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

Answer 17

If A is an elementary square matrix.

Answer 18

y did we just do that?

Answer 19

ohhhh cuz we are going backwards?

Answer 20

Now write \( A= I_n A \)

Answer 21

Not getting this stuff at all

Answer 22

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.

Answer 23

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

Answer 24

ok so show sth an example plz

Answer 25

I am too tired for a Latex example now :(

Answer 26

LOL Oh u r so annoying

Answer 27

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.

Answer 28

ok

Answer 29

That's an nice example Jemurray.

Answer 30

lol

Answer 31

*a

Answer 32

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Answer 33

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Answer 34

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Answer 35

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Answer 36

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Answer 37

I am evolving :P

Answer 38

LOL I guess me too

Answer 39

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Answer 40

LOL uhhhh no!
Did u see what i answered tanusingh

Answer 41

in math chat

Answer 42

no i didn't

Answer 43

so go check lol

Answer 44

lol

Answer 45

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Answer 46

Obviously I am evolving very slowly :P

Answer 47

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Answer 48

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Answer 49

ya

Answer 50

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Answer 51

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Answer 52

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Answer 53

How am I suppose to know? lol

Answer 54

idk

Answer 55

u know dont be stupid

Answer 56

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Answer 57

lol

Answer 58

LOL me too

Answer 59

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Answer 60

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Answer 61

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Answer 62

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Answer 63

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Answer 64

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Answer 65

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Answer 66

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Answer 67

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Answer 68

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Answer 69

who is star and ever1?

Answer 70

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Answer 71

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Answer 72

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Answer 73

FOOOOLLLLL I figured out what to do LOL

Answer 74

u have digressed frm d topic