1. Limited time only! Sign up for a free 30min personal 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!

Find eigenvalue for matrix B= {[3,4,12],[4,-12,3],[12,3,-4]}

  1. May 12, 2013 #1
    1. The problem statement, all variables and given/known data

    Find eigenvalue for matrix B= {[3,4,12],[4,-12,3],[12,3,-4]}

    2. Relevant equations



    3. The attempt at a solution

    I set up the charactersitic polynomial and got the equation:
    Pa(x) = (x-3)(x+12)(x+4) = x3 + 132 - 144 + 144 = x3 + 132

    So I have 3 eigenvalues: 0, 13, -13. Is this correct?
     
  2. jcsd
  3. May 12, 2013 #2
    Actually I forgot to calculate teh determinants so I got:

    Pa(x) = (x-3)(x+12)(x+4) + 2197 = x3 + 13x2 + 2053
     
  4. May 12, 2013 #3
    Those are the correct eigenvalues (if it is conventional to include 0 in your class). It may be good to note multiplicity of eigenvalues.
     
  5. May 12, 2013 #4
    From the characteristic polynomial x3 + 13x2 + 2053, how do I get the correct eigenvalues?
     
  6. May 12, 2013 #5

    Mark44

    Staff: Mentor

    Two of them are correct, but 0 is not an eigenvalue. It should be -13 (a repeated eigenvalue).

    You can't, since this isn't the correct characteristic polynomial. The eigenvalues are the roots of the characteristic polynomial.
     
  7. May 12, 2013 #6
    Okay I understand. So my eigenvalues are 13 and -13. If I was asked to find the basis for both of these, how do I go about doing that. I tried to solve the equation [13I2 - A I 0] however if ran into a wall. I row reduced it to get the matrix = {[2, 2/5, 6/5], [0,1,3], [0,0,1]}. But I wasnt sure where to go from there
     
  8. May 12, 2013 #7

    Mark44

    Staff: Mentor

    You should be solving the matrix equation (13I3 - A)x = 0, or equivalently, (A - 13I)x = 0.
    This would be the work to find the eigenvector for λ = 13.
    This is incorrect. Show me the matrix you started with, and a step or two of your work.
     
  9. May 12, 2013 #8
    (A - 13I)x = 0:

    {[10, 4, 12, 0],[4, 1, 3, 0],[12, 3, 17]} = {[1, 2/5, 6/5],[4, 1, 3, 0],[12, 3, 17, 0]} = {[1, 2/5, 6/5, 0], [0, -3/5, -9/5, 0],[0, -9/5, 13/5, 0]} = {[1, 2/5, 6/5, 0],[0, 1, 3, 0], [0, 0, 8, 0]}
     
  10. May 13, 2013 #9

    Mark44

    Staff: Mentor

    You started off with an incorrect matrix.

    Here is A:
    $$ \begin{bmatrix} 3 & 4 & 12\\ 4 & -12 & 3 \\ 12 & 3 &-4 \end{bmatrix}$$
    To get A - 13I, subtract 13 from the entries on the main diagonal.
     
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: Find eigenvalue for matrix B= {[3,4,12],[4,-12,3],[12,3,-4]}
Loading...