Find elementary matrix E such that B=EA

[subopolois]

Homework Statement

im having problems with this question, i don't 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

Homework Equations

elementary row operations

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 don't 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 \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.

 

[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.