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Math Help - invertible and diagonalized matrix

  1. #1
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    invertible and diagonalized matrix

    Given the matrix A=[29,18][-50,-31] explain why there is no invertible matix P that diagonalizes A.

    So I've solved for the eigenvalue and found that it is x2=[-3/5][1] and the A^-1 is [1/29,0][5/3,29/30]. Thank you in advance for your help.
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Re: invertible and diagonalized matrix

    Quote Originally Posted by nivek0078 View Post
    Given the matrix A=[29,18][-50,-31] explain why there is no invertible matix P that diagonalizes A.
    The only eigen value of A is \lambda=-1 (double) and \dim V_{-1}=2-\mbox{rank}(A+I)=2-1=1\neq \mbox{multiplic.}(-1). That is, A is not diagonalizable or equivalently, there is no P invertible such that P^{-1}AP=D (diagonal).
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    Re: invertible and diagonalized matrix

    Thank you for explaining that. It makes sense using the rank to solve it.
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