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anonymous
 one year ago
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 41 0) = (2 2)
(1 60 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?
anonymous
 one year ago
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 41 0) = (2 2) (1 60 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
 one year ago
Best ResponseYou've already chosen the best response.0I 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
 one year ago
Best ResponseYou've already chosen the best response.0I 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
 one year ago
Best ResponseYou've already chosen the best response.0Method 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.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Method 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
 one year ago
Best ResponseYou've already chosen the best response.0ok, 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
 one year ago
Best ResponseYou've already chosen the best response.0Does it connect to the GaussJordan elimination method ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oh, 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
 one year ago
Best ResponseYou've already chosen the best response.1dw:1434333153086:dw Here are some details. Hope this helps.

ybarrap
 one year ago
Best ResponseYou've already chosen the best response.1dw:1434333759397:dw http://www.wolframalpha.com/input/?i=inverse+%7B%7B2%2C4%7D%2C%7B1%2C6%7D%7D