Diagonalizing a matrix with repeated eigenvalues

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Today we will be diagonalizing a 3x3 matrix with repeated eigenvalues. Leave a problem in the comments below for me to work next week!

"Fireside"
Instrumental by Homage

Outro:
"Lateralus" as performed by Sakis Strigas
Originally by Tool

My current equipment for making videos (affiliate links):

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For the music in the video, please check the link in the description, and completely ignore the bullshit copyright claim.

EpicMathTime
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if you want to invert any matrix just turn it upside down smh and just erase the off diagonal elements to diagonalize it

AndrewDotsonvideos
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Co-factor expansion. Just learned this in my linear class!

joejo
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Dang, thanks dude, I didn't think of the possibility of two solutions of eigenvectors for a single eigenvalue.

linkmaster
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Can you make a video on the residue theorem and it's proof?

nanocount
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this is more of a challenge than anything, but you could try to solve the infamous Question 6 from the math olympiads.

filippodilascio
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Diagonalizable is my new favorite word

liesalllies
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Your video set up is an isomorphism v: your point of view --> our point of view in R^2. :P

Taricus
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nice video gym guy! one question: 6:45 why cannot we pick v1 also = 0? and why the way you pick just made your Q symmetric? Thanks a lot!

Tyokok
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You look so familiar... Oh wait, you're the buff version of langfocus.

gdsfish
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at 7:25 how to choose the order of eigenvectors of 5 in the Q matrix?

vijaysinghchauhan
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question: does wearing gymshark at my math test improve my grade?

Rien--