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!

Linear algebra adjoint proof question

  1. Mar 2, 2013 #1
    1. The problem statement, all variables and given/known data

    I dont understand how line five counting from the top in the attached image. How does det (A^-1 det A) become (detA)^n? I get that the A^-1 was factored out but I dont get how (detA )= (detA)^n. Thank you...

    http://img28.imageshack.us/img28/8742/20130302114549.jpg [Broken]




    Uploaded with ImageShack.us
    2. Relevant equations

    Properties of determinates?

    3. The attempt at a solution

    This is the only part of the proof I dont get and i dont know what rule is det A det equal to...
     

    Attached Files:

    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Mar 2, 2013 #2

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    hi baird.lindsay! :smile:

    (try using the X2 button just above the Reply box :wink:)
    it doesn't, it becomes (detA)n times det(A-1)

    this is because, for any number k and for any matrix M, det (kM) = kndet(M) :wink:

    (and detA is a number)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Linear algebra adjoint proof question
Loading...