# Find elementary matrix E such that B=EA

1. Nov 8, 2008

### 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

2. Nov 8, 2008

### gabbagabbahey

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

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

3. Nov 8, 2008

### HallsofIvy

Staff Emeritus
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.