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- anonymous

elementary matrix. I think it has something to do with the column but i thought it had to be row operstions
Question: find an elementary matrix E such that AE=B
i am given A = 2 4
1 6
B= 2 -2
1 3
i set it up like
(2 4|1 0) = (2 -2)
(1 6|0 1) (1 3)
the 2 and 1 are good but i cant do anything to the 4 and 6 without changing the 2 and 1 which i want to leave. Any thoughts?

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- anonymous

- schrodinger

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- anonymous

I have no idea what method you're using but here's a different perspective on it.
You're looking for a matrix E that verifies AE=B.
There's two easy ways to solve this.

- anonymous

I dont know if there is a name for it but basically i have matrix A and am using the identity matrix next to it. i think im supposed to do row operations on the Matrix A and do the same to the identiy matrix until it equals Matrix B

- anonymous

Method 1
First and foremost figure the dimensions of E - since A and B are two 2x2 matrixes then it's pretty clear that E will also be a 2x2 matrix.
Let x1,x2,x3 and x4 be the elements of that 2x2 matrix.
By solving AE and then equating that to each respective value of B you will get a linear system of 4 equations with 4 unknown variables (x1,x2,x3 and x4) which should be pretty easy to solve.

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- anonymous

Method 2
This implies knowing about the inverse of matrixes.
We work on the same deduction that E is a 2x2 matrix with elements x1,x2,x3 and x4 but instead of making equations out of it we could use a neat trick with the inverse matrix of A.
Let A^(-1) be the inverse of matrix A.
By multiplying A^(-1) to the "left" side of the equation we have that
A^(-1)*A*E=A^(-1)*B
But as we all know, the inverse of a matrix multiplied with the matrix itself is the identity matrix - which never changes anything about any matrix when multiplied to it.
E=A^(-1)*B
So all you need to do now is to find the inverse of the matrix A (that is A^(-1) ) and multiply it with B and then x1,x2,x3 and x4 will equal each corresponding member of that.

- anonymous

ok, i think thats kind of what i was doing. with the identity matrix. but i was thinking row operations or something. at least thats what my book did. but im going to try it your way.

- anonymous

Does it connect to the Gauss-Jordan elimination method ?

- anonymous

yes

- anonymous

Oh, well - if your teacher really insist on you using that then I suppose you can determine A^(-1) using that method as to prove to him/her that you know the method.

- ybarrap

|dw:1434333153086:dw|
Here are some details.
Hope this helps.

- ybarrap

|dw:1434333564364:dw|

- ybarrap

|dw:1434333759397:dw|
http://www.wolframalpha.com/input/?i=inverse+%7B%7B2%2C4%7D%2C%7B1%2C6%7D%7D