A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 5 years ago
How do I find the eigenvectors of the following matrix?
anonymous
 5 years ago
How do I find the eigenvectors of the following matrix?

This Question is Closed

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

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0first 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

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0by the way .. the eigenvector cant be zero.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0example for the eigenvectors are : 2v2 = v1 > (2,1) v2 = 2v1 >(1,2)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0please tell me if it is fine..

anonymous
 5 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!!

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

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0oh im glad that you answered eventually :)

anonymous
 5 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 \[v_2=2v_1\]??

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0if you take v1 = 1 then v2 = 2 (1,2) its the opposite from yours

anonymous
 5 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 :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Never mind, I got it :)
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.