1. Not finding help here? Sign up for a free 30min 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!

Need Help On Eigenvalue and Eigenvector

  1. Nov 27, 2006 #1
    Hi Guys,

    I have got some enquires for eigenvalue and eigenvector.

    Consider the 1st matrix:

    A = [ 1 2 3]
    [ 0 5 6]
    [ 0 6 5]

    The characteristic polynomial is

    det(A-λI) = [ 1-λ 2 3]
    [ 0 5-λ 6]
    [ 0 6 5-λ]

    = (1-λ) [ (5-λ)^2 - 36]

    The eigenvaules are D(λ) = 0 ---> λ1 = 1, λ2=-1 and λ3 =11
    May i know how do we get the λ1 , λ2 and λ3? Can someone advise me?
    Dont seem quadratic is working for this??


    Matrix (2)

    A = [3 5 3]
    [0 4 6]
    [0 0 1]

    Is the characteristic polynomial: det(A - λI) = [ 3-λ 5 3]
    [ 0 4-λ 6]
    [ 0 0 1-λ]

    = (3-λ)[(4-λ)(1-λ)- 0]?


    Does the characteristic polynomial of matrix 2 also the same as Matrix (3)

    A = [ 3 0 0]
    [ 4 4 0]
    [ 5 6 1]

    Please advise. Thanks :)
     
  2. jcsd
  3. Nov 27, 2006 #2
    When you take the det of a 3x3 matrix, you can take the elements of ANY row or column and multiply them by the 2x2 determinants you get from removing the row and column that that element is in, not forgetting the signs, which follow the

    (+-+...)
    (-+-...)
    (+-+...)

    pattern, I forget what it's called. So for those matrices, with their handy 0s in the right places, you can use the rows or columns with the two zeros in, which simplifies things a great deal.
     
  4. Nov 27, 2006 #3
    Thanks! How about the eigenvaules are D(λ) = 0 ---> λ1 = 1, λ2=-1 and λ3 =11
    May i know how do we get the λ1 , λ2 and λ3? Can someone advise me?
    Dont seem quadratic is working for this??
     
  5. Nov 27, 2006 #4
    You're on the right track. Now just do what you did for the whole thing, instead of having 3 different matrixes.
     
    Last edited: Nov 27, 2006
  6. Nov 27, 2006 #5
    Can you kindly advise how to get the values of
    λ1 = 1, λ2=-1 and λ3 =11? As i dun seem to get it.
     
  7. Nov 27, 2006 #6
    Do what you did to get the characteristic polynomials, just do it for the entire 3 x 3 matrix. From there you will get an expression with λ^3. Then set the characteristic polynomial = 0. The roots of the characteristic polynomials are nothing more than your λ's.
     
  8. Nov 27, 2006 #7
    det(A-λI) = [ 1-λ 2 3]
    [ 0 5-λ 6]
    [ 0 6 5-λ]

    = (1-λ) [ (5-λ)^2 - 36]

    This work you have done is exactly right. Now set this = 0. And find what your λ's are.

    Edit: This IS right, and this is all you need. You have to figure out why. In order to do this you have to know how to take a determinant of an entire 3*3 matrix.
     
    Last edited: Nov 27, 2006
  9. Nov 28, 2006 #8
    Thanks! I understand it now.
    I have another question:

    [ 2 2 3]a]
    [ 0 6 6]b] = 0
    [ 0 6 6]c]

    How do i find [a]

    [c] ?
    plz advise as i pretty poor in matrix.
     
  10. Nov 28, 2006 #9
    2(a) + 2(b) + 3(c) = d11
    0(a) + 6(b) + 6(c) = d21
    0(a) + 6(b) + 6(c) = d31

    You want the whole thing = 0. So you want d11 = d22 = d33 = 0.
     
  11. Nov 28, 2006 #10
    Hi Kogs,

    Do u hv msn? can i msn u to ask something awhile?
    Thanks!
     
  12. Nov 28, 2006 #11
    I'd rather just talk here. What do you need?

    I misread the original thing. I guess only d21 = 0. But you will notice d21 = d31.
     
  13. Nov 28, 2006 #12
    Thanks. But the answer for for [a
    b
    c]
    is [1
    0
    0]

    any idea how to get [1
    0
    0]?
    please advise. Thanks!
     
  14. Nov 28, 2006 #13
    I must be reading the question wrong then. Because that answer doesn't look right.
     
  15. Nov 28, 2006 #14
    i will scanned the notes and u hv a look ...cheers :)
     
  16. Nov 28, 2006 #15
    Here's the note :)
    the one circled, may i know how to get it? Please advise. Thanks!
     

    Attached Files:

  17. Nov 28, 2006 #16
    Can you post on website somewhere?
     
  18. Nov 28, 2006 #17
  19. Nov 28, 2006 #18
    No it does not.
     
  20. Nov 28, 2006 #19
    i re-attached again
     

    Attached Files:

    • pic.jpg
      pic.jpg
      File size:
      22.5 KB
      Views:
      63
  21. Nov 28, 2006 #20
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Need Help On Eigenvalue and Eigenvector
  1. System of equations (Replies: 10)

Loading...