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feldy90
 3 years ago
How do I find the eigenvectors of the following matrix?
feldy90
 3 years ago
How do I find the eigenvectors of the following matrix?

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feldy90
 3 years ago
Best ResponseYou've already chosen the best response.0\[A=\left[\begin{matrix}1 & 2 \\ 2 & 2\end{matrix}\right]\]

Coolsector
 3 years ago
Best ResponseYou've already chosen the best response.3first 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

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

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

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

feldy90
 3 years ago
Best ResponseYou've already chosen the best response.0Sorry  I have actually left my books for a moment... I will definitely check this when I get back to them  thanks so much!!

feldy90
 3 years ago
Best ResponseYou've already chosen the best response.0Totally forgot about this! Thank you so much  that was perfect!

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

feldy90
 3 years ago
Best ResponseYou've already chosen the best response.0Haha, 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 \[v_2=2v_1\]??

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

feldy90
 3 years ago
Best ResponseYou've already chosen the best response.0So 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 :)

feldy90
 3 years ago
Best ResponseYou've already chosen the best response.0Never mind, I got it :)
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