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!

How do I find the eigenvalue given unknown rows & eigen vect

  1. Oct 21, 2016 #1
    1. The problem statement, all variables and given/known data
    Consider the following matrix A (whose 2nd and 3rd rows are not given), and vector x.

    A =
    4 4 2
    * * *
    * * *
    x =
    2
    -1
    10

    Given that x is an eigenvector of the matrix A, what is the corresponding eigenvalue?

    2. Relevant equations


    3. The attempt at a solution

    4−λ 4 2
    a b−λ c
    d e f−λ=

    det (λI3-3) =

    −λ3+b+f+4×λ2+4×a−4×b+2×d+c×e−b×f−4×f×λ+−2×b×d+4×c×d+2×a×e−4×c×e−4×a×f+4×b×f

    Don't know if I'm on the right track. Trying to find the roots of this characteristic equation, but there's so many unknowns.
     
  2. jcsd
  3. Oct 21, 2016 #2

    fresh_42

    Staff: Mentor

    What is a eigenvector?
     
  4. Oct 21, 2016 #3
    An eigenvector of A is a non-zero vector x such that Ax = λx
     
  5. Oct 21, 2016 #4

    fresh_42

    Staff: Mentor

    So. Have you already computed Ax?
     
  6. Oct 21, 2016 #5
    Yes

    24 a2-b+c10 d2-e+f10
     
  7. Oct 21, 2016 #6

    I have 5 minutes left to answer the question. Would you mind helping me with the answer, and then you can explain it to me?
     
  8. Oct 21, 2016 #7

    fresh_42

    Staff: Mentor

    I assume, this should be a column vector. Now what says the equation ##Ax = \lambda x## in the first coordinate?
     
  9. Oct 21, 2016 #8
    Sorry? You mean 24?
     
  10. Oct 21, 2016 #9
    I got it! Thanks!
     
  11. Oct 21, 2016 #10

    fresh_42

    Staff: Mentor

    I mean the first coordinate is 24 on the left and ##\lambda x_1## on the right, yes.
     
  12. Oct 21, 2016 #11
    I figured it out, thanks a bunch!
     
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: How do I find the eigenvalue given unknown rows & eigen vect
Loading...