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Eigenvalues of 2x2 matrix

  1. Nov 15, 2015 #1
    1. The problem statement, all variables and given/known data
    Find the eigenvalues of the matrix
    ##
    \left( \begin{array}{cc}
    3 & -1.5\\
    -1.5 & -1\\
    \end{array} \right)
    ##
    It's probably a really stupid mistake, but the answer I get doesn't match the answer from wolfram alpha's eigenvalue calculator... always a bad sign.
    2. Relevant equations


    3. The attempt at a solution
    The characteristic equation is:
    (3-λ)(-1-λ) -##\frac{9}{4}## = 0
    → λ2-2λ - ##\frac{21}{4}## = 0
    Using the quadratic formula,

    λ = ##\frac{2 \pm \sqrt{4 - (4\times -\frac{21}{4})}}{2}##
    = ##1 \pm \sqrt{25}##
    = 6 or -4.

    But apparently, I should be getting -1.5 and 3.5 . I have checked it so many times to see where I've gone wrong! What's the mistake??
     
  2. jcsd
  3. Nov 15, 2015 #2

    vela

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    The 2 in the denominator divides into the entire numerator. You appeared to cancel it with the 2 from the -b part of the numerator, but ignored the rest of the numerator.
     
  4. Nov 15, 2015 #3

    fresh_42

    Staff: Mentor

    you lost 1/2 calculating λ. It's √25 / 2 and not √25

    ##\frac{a + b}{c} = \frac{a}{c} + \frac{b}{c}##
     
  5. Nov 15, 2015 #4
    You wouldn't believe how long I stared a that question. And didn't spot it. Thanks, I was getting so frustrated!
     
  6. Nov 15, 2015 #5

    fresh_42

    Staff: Mentor

    that happens sometimes and the honest of us aren't afraid to admit that it happens to them as well from time to time
     
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