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Homework Help: Eigne values

  1. Nov 2, 2005 #1
    Hi, I need help for this problem:
    Find the eignevalues and eingenvectors for the matrix below. DO NOT compute them directly by computing the matrix:
    A-1

    We need to find some kind of demonstration to see if the eignevalues of A-1 are the same, opposite or inverse (or whatever) as those of matrix A
    Suppose that the eignvalues are 1,2,3 and the eignvectors are [1,1,0], [0,1,0],[ 3,-1,2] ( in columns
    Thank you
    B
     
  2. jcsd
  3. Nov 2, 2005 #2

    HallsofIvy

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    Science Advisor

    If [tex]Ax= \lambda x[/tex] Then [tex]A^{-1}Ax= A^{-1}\lambda x= \lambda A^{-1}x[/tex].

    What does that tell you?
     
  4. Nov 2, 2005 #3
    I have been thinking but I really do not know.
    Can we say that I ( indentity matrix)= lambda*A-1??
    I does make me go far doesn't it?
     
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