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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.
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
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.
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.
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.
Does it connect to the Gauss-Jordan elimination method ?
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.
|dw:1434333153086:dw| Here are some details. Hope this helps.