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Math Help - Eigenvalues, Eigenvectors, Inverse matrix- am i on the right track?

  1. #1
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    Question Eigenvalues, Eigenvectors, Inverse matrix- am i on the right track?

    Question: suppose that A is an invertible matrix (i.e. A^(-1) ), and that x is an eigenvector for A with eigenvalue ⅄ ≠ 0. Show that x is an eigenvector for A^(-1) with the eigenvalue ⅄^(-1) (inverse ⅄).

    My answer:

    By: Ax = b, therefore: x = A^(-1) b

    When a matrix A and a nonzero vector x satisfy : Ax = ⅄x (for some scalar ⅄), and by: x = A^(-1) b,

    then: x = (A^(-1)) ⅄x,

    therefore: (⅄^(-1))x = (A^(-1))x

    Am i right? or at least on the right track?
    please and thankyou
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  2. #2
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    that is good

    Yes , your derivation is correct
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