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Math Help - Eigenvalues help

  1. #1
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    Eigenvalues help

    Hello, I'm having a little trouble solving this question:
    "Let A have 0,3 and 5 as eigenvalues and the independent eigenvectors u, v and w.Find a particular solution to Ax=v+w.Find all the solutions."
    Could you guys give me a hint or solve it?Thanks
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Re: Eigenvalues help

    Hint:

    A\left(\frac{1}{3}v+\frac{1}{5}w\left)=\frac{1}{3}  Av+\frac{1}{5}Aw=\frac{1}{3}3v+\frac{1}{5}5w=v+w

    that is, x=\frac{1}{3}v+\frac{1}{5}w\left is a particular solution. Try the rest.
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