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Math Help - Finding Eigenvalues (with a variable)

  1. #1
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    Finding Eigenvalues (with a variable)

    So I have the matrix
    A=\left(\begin{matrix} 2/5 &1/5\\x &0\end{matrix}\right)
    And it asks me to find the eigenvalues (as expressions in the parameter x)
    So using λ=Lambda I got: λ^2-(2/5)λ-(1/5)x. How am I supposed to factor that to find the eigenvalues when x is there?
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Re: Finding Eigenvalues (with a variable)

    Quote Originally Posted by calculuskid1 View Post
    So using λ=Lambda I got: λ^2-(2/5)λ-(1/5)x. How am I supposed to factor that to find the eigenvalues when x is there?
    Solving the quadratic equation \lambda^2-(2/5)\lambda -(1/5)x=0 you'll obtain \lambda=\frac{1\pm \sqrt{1+5x}}{5} .
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  3. #3
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    Re: Finding Eigenvalues (with a variable)

    Thank you! I'm not sure why I didn't think to use the quadratic formula! I always forget to go back to basic principles lol
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