anonymous
  • 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?
Linear Algebra
schrodinger
  • schrodinger
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anonymous
  • 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
  • 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
  • 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
  • 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
  • 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
  • anonymous
Does it connect to the Gauss-Jordan elimination method ?
anonymous
  • anonymous
yes
anonymous
  • 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
  • ybarrap
|dw:1434333153086:dw| Here are some details. Hope this helps.
ybarrap
  • ybarrap
|dw:1434333564364:dw|
ybarrap
  • ybarrap
|dw:1434333759397:dw| http://www.wolframalpha.com/input/?i=inverse+%7B%7B2%2C4%7D%2C%7B1%2C6%7D%7D