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Very Simple Eigenvalue Calculation Need explanation please

  1. Dec 1, 2012 #1
    1. The problem statement, all variables and given/known data

    Calculate the eigenvalues of the matrix
    5 2
    -3 0



    2. Relevant equations



    3. The attempt at a solution

    Ok we were taught that eigenvalues were calculated by taking the determinant( A - λI) = 0. So just subtract a "λ" value from the diagnol entries of the given matrix... so why aren't the eigenvalues 5 and 0? Please help me understand why the e values are 2 and 3?
     
  2. jcsd
  3. Dec 1, 2012 #2

    Ray Vickson

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    What is the determinant of the matrix A - λI? What is the equation you get when you set this determinant to zero?

    Besides: see what you get when you try to solve the equation Ax = 5x; that will tell you why 5 is not an eigenvalue.
     
  4. Dec 1, 2012 #3

    vela

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    I have to ask: Why do you think the eigenvalues would be 5 and 0?
     
  5. Dec 1, 2012 #4
    I just realized that I butchered my algebra and now see that det(A- xI) = 0

    (5-x)(-x) - (-6) = x^2 -5x + 6 = 0
    (x-2) (x-3) = 0
    x=2,3

    Thanks for reminding me though appreciate it!
     
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