Loser66
  • Loser66
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
Mathematics
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Loser66
  • Loser66
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
Mathematics
schrodinger
  • schrodinger
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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zzr0ck3r
  • zzr0ck3r
I forget this stuff. Do you need to diagonalize A first?
Loser66
  • Loser66
I am looking at my Discreet notes, now. Actually, it is from DE
Loser66
  • Loser66
hey barbecue, any idea??

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zzr0ck3r
  • zzr0ck3r
lol
anonymous
  • anonymous
I forget do i find reduced row echelon form for 1?
Loser66
  • Loser66
eigenvalues of A are a and c
anonymous
  • anonymous
i don't know what I'm doing lol
Loser66
  • Loser66
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
Loser66
  • Loser66
Assume they are correct, then Diagonalization of A , namely \(D=\left[\begin{matrix}a&0\\0&c\end{matrix}\right]\) We get \(e^{At }= P*\left[\begin{matrix}e^{at}&0\\0&e^{ct}\end{matrix}\right]*P^{-1}\)
Loser66
  • Loser66
But I need confirm the eigenvalues before going further. @dan815 contribute, please
Loser66
  • Loser66
Then, we just do matrix multiplication to get the answer. ha!! but this knowledge is from Discreet, not from DE.

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