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Homework Help: Eigenvalu problem

  1. Apr 4, 2010 #1
    The problem statement, all variables and given/known data
    [PLAIN]http://img14.imageshack.us/img14/7826/70745131.jpg [Broken]

    The attempt at a solution
    How do I go about solving this problem?
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Apr 4, 2010 #2
    2..
    is dis correct!
     
  4. Apr 4, 2010 #3
    ????
     
  5. Apr 4, 2010 #4

    Mark44

    Staff: Mentor

    Maybe, maybe not.
     
  6. Apr 4, 2010 #5

    Mark44

    Staff: Mentor

    What does it mean to say that a number lambda is an eigenvalue of a matrix?
     
  7. Apr 4, 2010 #6
    it means that no. is the eigen value of new matrix formed by the expression..
    A^2010 -2A+3I
     
  8. Apr 4, 2010 #7
    if for an eigen vector,eigen value is 1...dis means for that e-vector, matrix is behaving like an identity matrix...so the same eigen vector this expression will have eigen value :2
     
  9. Apr 4, 2010 #8
    How did you show it was 2?
     
  10. Apr 4, 2010 #9

    Mark44

    Staff: Mentor

    You didn't answer my question. Here's a slightly different question. What does it mean to say that 3 is an eigenvalue of a matrix A?
     
  11. Apr 4, 2010 #10
    matrix can act in two ways ...rotating a vector or changing it length...
    this value...(e-value) is a factor by which matrix changes the length of vector...
     
  12. Apr 4, 2010 #11
    hope this give answer to your question!
     
  13. Apr 4, 2010 #12

    Mark44

    Staff: Mentor

    I'm looking for an equation that involves A and 3.
     
  14. Apr 4, 2010 #13
    Is it:

    (A - 3I)x = 0
     
  15. Apr 4, 2010 #14

    Mark44

    Staff: Mentor

    Yes, or equivalently, Ax = 3x.

    With your problem, you know that 1 is an eigenvalue of A, so Ax = 1x. You are trying to find an eigenvalue of A2010 - 2A + 3I.

    (A2010 - 2A + 3I)x = ?x
     
  16. Apr 5, 2010 #15

    Mark44

    Staff: Mentor

    Think about the other problem you posted. If Ax = 1x, what are A2x, A3x, A4x, ...?
     
  17. Apr 5, 2010 #16
    All would be 1x
     
  18. Apr 5, 2010 #17

    Mark44

    Staff: Mentor

    OK, so what would (A2010 - 2A + 3I)x be?
     
  19. Apr 5, 2010 #18
    Also 1x
     
  20. Apr 5, 2010 #19

    Mark44

    Staff: Mentor

    No it isn't.
     
  21. Apr 5, 2010 #20
    Whoops lol, I meant 2.
     
  22. Apr 5, 2010 #21
    So would it be enough to say that since A=1, A^2010 - 2A + 3I = 1 -2 + 3 = 2?
     
  23. Apr 5, 2010 #22

    Mark44

    Staff: Mentor

    No, A is a matrix, so it can't be equal to any number, and A^2010 - 2A + 3I [itex]\neq[/itex] 2

    However, you know that Ax = 1x, so (A2010 - 2A + 3I)x = ___x? (Fill in the blank.)
     
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