Question

When finding eigenvectors, what do you do when you reach a dead end like this? (example shown in comment)

Answer 1

(-6 1)
(0 -6) Lets say thats a matrix haha.....

Answer 2

so solving for the eigenvalues, I got lamda(1,2)= -6
Then trying to make the eigenvector got me to
0n_1=n_2

Answer 3

and i'm not sure how to proceed

Answer 4

I got double root L =6. not -6. can you check and we work together?

Answer 5

hmm....(-6-L)^2...wouldnt L=6 give you (-6-(6))^2=(-12)^2
I go tthat first too

Answer 6

what is your characteristic equation? mine is L^2 -12L +36 = (L -6)^2 =0 ---> l =6

Answer 7

oh, sorry, you are right, my bad.

Answer 8

so, L = -6 and replace to matrix Ax -Lx

Answer 9

wait no, I did what you said and now im torn....
If you find the DET you get (-6-L)(-6-L), which is (-6-L)^2.....(obviously haha)
but if you multiply them together you get (L^2+12L+36), which could be turned into (L+6)^2, thus making you right......HHHOOOWW?

Answer 10

OOOHH no nvm its -12L not +.....ok, so its L=-6....now what haha

Answer 11

hahaaha... so weird . I am confused many times, when my discrete pro asks me using L-A while linear prof said that I must come up with A -L

Answer 12

ok, anyway, it's yours, you check and choose which one is right, then we move.

Answer 13

shoot i just got yours again....whatever, lets move on and Ill try both (I have unlimited attempts so its all good!)

Answer 14

hi guy!! your brother must go somewhere to eat something, I cannot stay here to witness you switch many times like that. I'll be back in 15 minutes. do it carefully

Answer 15

alright enjoy your meal, I got my final answer, and it's still L=-6. But I really just need to know how to go about turning that into and eigenvector and a generalized eigenvector. thanks for your help so far

Answer 16

so, i guessed
(1)
(0) is my v_1


(0)
(1) is my "generalized" eigenvector

Answer 17

to count eigenvector, you use the matrix