find elementary matrix E such that B=EA

subopolois

1. The problem statement, all variables and given/known data
im having problems with this question, i dont know how they got their answer. the question is: find elementary matrix E such that B=EA
A=-1 2 B= 1 -2 (these are matrices)
0 1 0 1


2. Relevant equations
elementary row operations


3. The attempt at a solution
-1 2|1 0 (row 1x-1) 1 -2|-1 0 (row 1+2 row 2) 1 0|-1 2
0 1|0 1 0 1|0 1 0 1|0 1

the answer in my book says its -1 0 but i dont know how they got that
0 1

gabbagabbahey

If you have learned about matrix inverses, the solution should be fairly simple...A quick calculation shows that [itex]\text{det}(A) \neq 0[/itex] and so its inverse exists...what do you get when you multiply both sides of the equation [itex]B=EA[/itex] from the right by [itex]A^{-1}[/itex]?

PS please try to use LaTeX for matrices here, your post is difficult to read.

HallsofIvy

More simply, an "elementary" matrix corresponds to a "row operation". Specifically, the elementary matrix corresponding to a given row operation is given by that row operation applied to the identity matrix.

Here, we get B from A by multiplying the top row by -1. Multiply the top row of the identity matrix by -1.