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Loser66

  • one year ago

1)Compute \(e^{At}\) where \(A=\left[\begin{matrix}a&o\\b&c\end{matrix}\right]\) 2) Find the eigenvalues and eigenvectors of \(e^{-A}\) Please, help

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  1. zzr0ck3r
    • one year ago
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    I forget this stuff. Do you need to diagonalize A first?

  2. Loser66
    • one year ago
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    I am looking at my Discreet notes, now. Actually, it is from DE

  3. Loser66
    • one year ago
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    hey barbecue, any idea??

  4. zzr0ck3r
    • one year ago
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    lol

  5. anonymous
    • one year ago
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    I forget do i find reduced row echelon form for 1?

  6. Loser66
    • one year ago
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    eigenvalues of A are a and c

  7. anonymous
    • one year ago
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    i don't know what I'm doing lol

  8. Loser66
    • one year ago
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    eigenvectors are \(\left(\begin{matrix}a-c\\b\end{matrix}\right)\) and \(\left(\begin{matrix}0\\1\end{matrix}\right)\) Not sure about the second one, someone checks, please

  9. Loser66
    • one year ago
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    Assume they are correct, then Diagonalization of A , namely \(D=\left[\begin{matrix}a&0\\0&c\end{matrix}\right]\) We get \(e^{At }= P*\left[\begin{matrix}e^{at}&0\\0&e^{ct}\end{matrix}\right]*P^{-1}\)

  10. Loser66
    • one year ago
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    But I need confirm the eigenvalues before going further. @dan815 contribute, please

  11. Loser66
    • one year ago
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    Then, we just do matrix multiplication to get the answer. ha!! but this knowledge is from Discreet, not from DE.

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