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

Question

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

zzr0ck3r · Answer

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

loser66 · Answer

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

loser66 · Answer

hey barbecue, any idea??

zzr0ck3r · Answer

lol

anonymous · Answer

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

loser66 · Answer

eigenvalues of A are a and c

anonymous · Answer

i don't know what I'm doing lol

loser66 · Answer

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 · Answer

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 · Answer

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

loser66 · Answer

Then, we just do matrix multiplication to get the answer. ha!! but this knowledge is from Discreet, not from DE.