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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

I forget this stuff. Do you need to diagonalize A first?

2. Loser66

I am looking at my Discreet notes, now. Actually, it is from DE

3. Loser66

hey barbecue, any idea??

4. zzr0ck3r

lol

5. anonymous

I forget do i find reduced row echelon form for 1?

6. Loser66

eigenvalues of A are a and c

7. anonymous

i don't know what I'm doing lol

8. 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

9. Loser66

Assume they are correct, then Diagonalization of A , namely $$D=\left[\begin{matrix}a&0\\0&c\end{matrix}\right]$$ We get $$e^{At }= P*\left[\begin{matrix}e^{at}&0\\0&e^{ct}\end{matrix}\right]*P^{-1}$$

10. Loser66

But I need confirm the eigenvalues before going further. @dan815 contribute, please

11. 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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