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feldy90Best ResponseYou've already chosen the best response.0
\[A=\left[\begin{matrix}1 & 2 \\ 2 & 2\end{matrix}\right]\]
 2 years ago

CoolsectorBest ResponseYou've already chosen the best response.3
first find eigenvalues :det(A  λI) = 0 λI  A = \[\left[\begin{matrix}1λ & 2 \\ 2 & 2λ\end{matrix}\right]\] so Det : (1−λ)(−2−λ)  4 = 0 λ^2  λ + 2λ 2 4 = 0 λ^2 +λ 6 = 0 λ^2 +3λ  2λ  6 = 0 λ(λ+3)  2(λ+3) (λ2)(λ+3) = 0 λ=3,2 now Av=λv Av = 2v v1+2v2 = 2v1 2v1 2v2 = 2v2 any vector of the form : 2v2 = v1 Av = 3v v1 + 2v2 = 3v1 2v1  2v2 = 3v2 2v2 = 4v1 any vector of the form : v2 = 2v1
 2 years ago

CoolsectorBest ResponseYou've already chosen the best response.3
by the way .. the eigenvector cant be zero.
 2 years ago

CoolsectorBest ResponseYou've already chosen the best response.3
example for the eigenvectors are : 2v2 = v1 > (2,1) v2 = 2v1 >(1,2)
 2 years ago

CoolsectorBest ResponseYou've already chosen the best response.3
please tell me if it is fine..
 2 years ago

feldy90Best ResponseYou've already chosen the best response.0
Sorry  I have actually left my books for a moment... I will definitely check this when I get back to them  thanks so much!!
 2 years ago

feldy90Best ResponseYou've already chosen the best response.0
Totally forgot about this! Thank you so much  that was perfect!
 2 years ago

CoolsectorBest ResponseYou've already chosen the best response.3
oh im glad that you answered eventually :)
 2 years ago

feldy90Best ResponseYou've already chosen the best response.0
Haha, later is better than never, right? :P Quick question, for the eigenvalue 3, is the final eigenvector\[v=\left(\begin{matrix}2 \\ 1\end{matrix}\right)\] Since \[v_2=2v_1\]??
 2 years ago

CoolsectorBest ResponseYou've already chosen the best response.3
if you take v1 = 1 then v2 = 2 (1,2) its the opposite from yours
 2 years ago

feldy90Best ResponseYou've already chosen the best response.0
So would the eigenspace of eigenvalue 2, be: \[span \left\{ \left(\begin{matrix}2 \\ 0\end{matrix}\right) ,\left(\begin{matrix}0 \\ 1\end{matrix}\right)\right\}\] or just \[span \left\{ \left(\begin{matrix}2 \\ 1\end{matrix}\right) \right\}\] Thanks for the ongoing help :)
 2 years ago

feldy90Best ResponseYou've already chosen the best response.0
Never mind, I got it :)
 2 years ago
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