1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Find elementary matrix E such that B=EA

  1. Nov 8, 2008 #1
    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. jcsd
  3. Nov 8, 2008 #2


    User Avatar
    Homework Helper
    Gold Member

    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.
  4. Nov 8, 2008 #3


    User Avatar
    Science Advisor

    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook