anonymous
  • anonymous
Turing????
Mathematics
  • Stacey Warren - Expert brainly.com
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
Hey
TuringTest
  • TuringTest
who wassup?
TuringTest
  • TuringTest
whoa*

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anonymous
  • anonymous
I am getting really confused
TuringTest
  • TuringTest
I hope I can help...
saifoo.khan
  • saifoo.khan
Chatting here? Use chat please. :D
anonymous
  • anonymous
LOL I need to find an inverse of a matrix
TuringTest
  • TuringTest
I anticipate a question officer ;)
saifoo.khan
  • saifoo.khan
As soon as i came, he started studying!!!
anonymous
  • anonymous
I learnt one way that you use kind of gauss elimination
anonymous
  • anonymous
|dw:1327265979609:dw| like this
TuringTest
  • TuringTest
Well there are quite a few ways to do that. I know you know at least one and I sent you a link on more. http://tutorial.math.lamar.edu/Classes/LinAlg/FindingInverseMatrices.aspx for instance theorem 4 on this page is what FoolForMath was going to use
anonymous
  • anonymous
wait a sec hold ur horses
TuringTest
  • TuringTest
do you want to do the one you have with the gauss-jordan thing? cuz the other way is faster and more reliable...
TuringTest
  • TuringTest
...for 2x2 at least
anonymous
  • anonymous
ik but i gotta use that way and i am really solving a 3 by 3 matrix
TuringTest
  • TuringTest
what do you mean you are really solving a 3x3 ?
anonymous
  • anonymous
the problem I am doing now is a 3by 3 matrix
TuringTest
  • TuringTest
oh, so you want to work out the inverse of the 3x3 with the same method?
anonymous
  • anonymous
|dw:1327266165384:dw|
TuringTest
  • TuringTest
well post it, though it's a pain to write out...
anonymous
  • anonymous
Well this is the method right?
TuringTest
  • TuringTest
yeah, that's the same method as before
anonymous
  • anonymous
ok well now I have another method and i wld like to know th edifference
anonymous
  • anonymous
http://stattrek.com/matrix-algebra/how-to-find-inverse.aspx This is the other method
anonymous
  • anonymous
It is so similar to the first one. how is it different?
TuringTest
  • TuringTest
Oh I hate this stupid way, I think it works best for computer programs. Conceptually it winds up being the exact same thing: using transformations to an identity matrix to tell you how to find the inverse of the original. This one just formalizes all the steps at the end into a big matrix product (all the E's). Since each matrix in the product transforms a matrix just like a step in your method, this amounts to the same thing, but allows you to write each step as a separate matrix. Like I say, I think it works best for programming the inverse of large matrices.
anonymous
  • anonymous
but wait isnt the last step the inverse. Like in the first method it was and in the seond methos it isnt. What are we doing different
anonymous
  • anonymous
It is like bothering me and I cant figure it out
TuringTest
  • TuringTest
Imagine you are doing your inverse the old way each step is the same as multiplying by one of those E matrices One way of formalizing the first method you learned is as\[AA^{-1}=I\]now let each step be a matrix E_n. We have to multiply both sides\[(E_1E_2...E_nA)A^{-1}=I(E_nE_{n-1}...E_1)\]the first group of terms is Identity matrix, because that's what we are supposing we do in your method, so we have\[IA^{-1}=I(E_nE_{n-1}...E_1)\]\[A^{-1}=E_nE_{n-1}...E_1\]I hope that demonstrates that they are essentially the same method if you look closely to what we did. The only difference is representing each step in the transformation with a matrix E_n
anonymous
  • anonymous
k wait let me ask u what is an e matrice?
anonymous
  • anonymous
I have a sneaky feeling i am doing something wrong here
TuringTest
  • TuringTest
it just represents one of the transformations that you do in order to get row-eschelon form. Look at the matrix in the example|dw:1327267298132:dw|now we add -2R1 to R2 for both this and the identity matrix, just as we would do with your earlier method...
anonymous
  • anonymous
But we r doing the same thing with the other method IDK i am sooo confused
TuringTest
  • TuringTest
|dw:1327267397287:dw|the only difference here is that now we are going to stop and take away our altered identity matrix and call it E1
anonymous
  • anonymous
do u have twidlla or aomething like taht?
TuringTest
  • TuringTest
|dw:1327267501628:dw|now you can check that multiplying\[E_1A\]will be the exact same effect as using -2R1+R2
TuringTest
  • TuringTest
yeah sure, this seems to be lagging, post a link to twiddla if you want
anonymous
  • anonymous
lol i dont have one do u ?
TuringTest
  • TuringTest
no...
TuringTest
  • TuringTest
Do you see what I'm saying though? Try multiplying the matrices (E_1)A and you will see it has the same effect as the row operation we did. So they are the exact same thing.
anonymous
  • anonymous
lol maybe i will have to reread it:D
anonymous
  • anonymous
I have skype and tehn we cld share screens
anonymous
  • anonymous
LOL U dont have too
TuringTest
  • TuringTest
Yeah, I did explain it rather clearly I think.. Look above, the first step in your old way produces a matrix|dw:1327267836351:dw|now stop and call this new matrix E1...
anonymous
  • anonymous
ok is e1 only the right side or the whole matrix
TuringTest
  • TuringTest
Each row operation makes a new matrix we call E from the identity matrix on the right|dw:1327267931741:dw|check that matrix multiplication of (E1)A=A2 in other words multiplying by the changed identity matrix is the same as the row operation.
TuringTest
  • TuringTest
typo* that should be 'check that (E1)A1=A2' above
anonymous
  • anonymous
okkkk got that so far
TuringTest
  • TuringTest
now we stop and write a new identity matrix instead of continuing on the same one as before that is the main difference here|dw:1327268217059:dw|and surprise surprise the new altered identity matrix after the last step will be called E2 again check that multiplying E2(A2)=A3 we repeat this process until we have the identity matrix on the left, each time with a new identity matrix on the right that we set aside and name after each row operation
TuringTest
  • TuringTest
|dw:1327268423853:dw|
anonymous
  • anonymous
wtf omg u clarified it for me
TuringTest
  • TuringTest
hooray! that's all I could ask for :D
anonymous
  • anonymous
LOL my book never explained that difference taht u sart a new matrix every time HAHA
anonymous
  • anonymous
I hate my book LOL
anonymous
  • anonymous
Oh man I am so excited Thanks
TuringTest
  • TuringTest
That's why you need people to communicate with. Books can't cater to people very well.
anonymous
  • anonymous
I have been trying to tackle this since yesterday evening LOL and noon ecld understand me
anonymous
  • anonymous
Ya i am studying online so I am having difficulties
anonymous
  • anonymous
Thanks turing u r awesome :DDDDD
TuringTest
  • TuringTest
anytime, thanks for refreshing my memory on this method :)

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