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Math Help - Finding matrices with a given eigenvector/eigenvalue

  1. #1
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    Finding matrices with a given eigenvector/eigenvalue

    Problem: Find all 2x2 matrices for which is an eigenvector with associated eigenvalue -1.

    Here's my attempt:











    This is where I start to get off track, assuming I was actually on the correct track. A push in the right direction would be great.

    Thanks.
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by tangibleLime View Post
    Problem: Find all 2x2 matrices for which is an eigenvector with associated eigenvalue -1.

    Here's my attempt:











    This is where I start to get off track, assuming I was actually on the correct track. A push in the right direction would be great.

    Thanks.
    One hundred percent correct, actually! Just solve those last two simultaneous equations!
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  3. #3
    MHF Contributor alexmahone's Avatar
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    2a+3b=-2

    b=-(2a+2)/3

    2c+3d=-3

    d=-(2c+3)/3

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  4. #4
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    Huzzah! Thanks, I got it.

    And thanks to alexmahone for confirming my answer.
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