Results 1 to 3 of 3

Math Help - Help solving a couple of questions with Linear Algebra

  1. #1
    Newbie
    Joined
    Jan 2013
    From
    Australia
    Posts
    2

    Help solving a couple of questions with Linear Algebra

    Hi there guys,
    I have tried and tried and tried. I can't seem to get anywhere with these questions, Just wondering if anybody here could help me out!
    Help solving a couple of questions with Linear Algebra-questions.jpg

    Any help would be great! Please and thank you!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Jan 2013
    From
    Australia
    Posts
    2

    Re: Help solving a couple of questions with Linear Algebra

    The matrix A, Being the general one
    [a,b
    c,d]

    Where Tr(A) = a+d and Det(A) is ad-bc
    Last edited by Adro232; January 2nd 2013 at 11:55 AM. Reason: Added info
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    Joined
    Dec 2012
    From
    Athens, OH, USA
    Posts
    709
    Thanks
    294

    Re: Help solving a couple of questions with Linear Algebra

    I think you neglected to mention that A is a 2 by 2 matrix! For any larger matrix, your result is generally false.

    For a 2 by 2 matrix, the characteristic equation is:
    t^2-tr(A)t+det(A)=0, and so Cayley Hamilton says A^2-tr(A)A+det(A)I=0
    So I={tr(A)A-A^2\over tr(A)} or I=AB with B={tr(A)I-A\over tr(A)}
    Don't you know then that this implies B=A^{-1}?

    The remaining questions should be easy using this form for A inverse.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Linear algebra questions
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: May 23rd 2012, 04:06 AM
  2. 2 Linear algebra questions
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: January 7th 2012, 03:06 AM
  3. couple Algebra questions
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: October 5th 2008, 02:27 PM
  4. Linear Algebra please help.Exam in a couple of hours.
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: June 20th 2008, 04:35 AM
  5. Solving equations, a couple questions!
    Posted in the Algebra Forum
    Replies: 5
    Last Post: January 20th 2007, 08:06 PM

Search Tags


/mathhelpforum @mathhelpforum