Diagonalizing 3x3 Matrix - Full Process [Passing Linear Algebra]

Important high-level asides:
1) 3:07 (remember, 1 ≤ geo mult ≤ alg mult, so since λ=1 has alg mult of 1, it's geo mult is automatically 1)
2) 6:15 (the point where we find out A is diagonalizable)
Finding Eigenvalues: 0:40
Finding Basis for Eigenspaces: 4:20
Putting it all together: 10:06

[@trapitusaventurez2190]

oof this exam tomorrow ain't looking too good.

[@trapitusaventurez2190]

knew how to do the full process of diagonalization, but got stuck before I could find the eigen values, because I couldn't factorize x^3-*x^2+21x-6 great:-)

[@JacobEriksson]

Aye same here man

[@prey_ssbm]

@@trapitusaventurez2190 I don't think that can be factorized. At least Symbolab can't do it.

[@alfredpeter2404]

I'm in the EXACT SAME situation, except I'm trying to figure out what happens at 7:10

[@nourhh_]

@@alfredpeter2404 SAME😭

[@jamesjanzen2604]

Man, wish I'd found this earlier into the semester, but these are still amazing videos. The style in this one, at least, is absolutely perfect: Explaining everything, still moving fast enough to stay interesting, making everything super clear without getting monotonous. So good.

[@Splashingrandom]

This is fantastic, loving your series. Thanks!!!

[@kyew5173]

Bruh u really saving lives out here

[@wilsongray4316]

Of all the videos about diagonalization, yours was the best to follow....thank you

[@scooterking136]

love this video, thank you! very helpful and you have a sense of humor

[@great9640]

you helped me so much lol, a concept that seemed so difficult ended up being: using 3 eigenvectors to make a new matrix. thanks you so much sir. till this day we appreciate your content!

[@safaebee2885]

thank you so much. you're really helping me through first year engineering.

[@Commenter839]

This channel actually slaps though, I appreciate how you get straight to the point on these videos. Sometimes I'm not looking for theory and I just want to see some calculations lol

[@jwliao6973]

I don't know how I can express my gratitude to you. By far best explanation I've ever seen.❤❤❤❤

[@mika2666]

Ok this is exactly what I needed thank you so much!

[@nourjandali]

That was awesome explanation. Thanks!

[@danielkim3525]

Thank you kind sir. You helped me greatly with my homework.

[@alishashoukat1682]

Ohh man you nailed it!! Amazing 🎉

[@khojanemoses9570]

This tutorial video is wonderful.

[@chestnutbaal3566]

thank you i was kinda lost but you helped me grasp the topic

[@gilthunder1737]

Very helpful sir thanks alot for explaining in such a simple words 😭❤️🌸🌹✨✨

[@andrii5054]

very helpful, thanks

[@prey_ssbm]

idk why but I found the "see what im saying" at 0:10 mad funny lmao

[@prey_ssbm]

Thanks a lot!

[@arsenal100100]

Thank you! You have no idea how much you've helped me

[@SosukeAizen9543]

awesome thanks a lot
you really helped unlike those of my deadbeat university teachers

[@aidanpitt5240]

You good sir are a king

[@kktk9707]

Thanks a lot, Sir.
I'm self-learning at home.
Your video is helping me for my exam.
🙏🙏🙏🙏

[@jayrocapela]

Thanks Tom Holand!

[@nomtomm]

SAVING ENGINEERING LIVES

[@MentalDog2601]

Thank you sir👍

[@ngonidzashekimbini7177]

Thanks mate

[@cristhianangelocalderoncor3340]

don't have to normalize eigenvectors before constructing the matrix C?

[@pisanghangus2]

thank u !

[@theonewhoknocks860]

thank you

[@1dred]

nice :)

[@bradywreed2725]

When finding the eigenvalue you found your characteristic polynomial to be (2-lambda)(lambda-2)(lambda-1). Wouldn't that make your eigenvalues -2,1, and 2? And then because your eigenvalues are equal to your eigenvectors wouldn't that make the matrix diagonalizable?

[@bayleaf2383]

i realize this is probably late for u but I don't want anyone seeing this in the future to be confused, but in lambda - 2 = 0 and 2 - lambda = 0, they'd both be 2, think u just made an algebraic mistake.

[@joeyjoe8023]

I don't the part where you jumped the steps in finding the linear independence

[@rinr3300]

I didn't get the row reduction r3+r1 and?

[@deli5777]

supposed to be PDP, c is used for constants haha. nice video though

[@crazygur1y]

tysm

[@perihanerdogan1133]

which grade are you in?

[@sushree4018]

Why to take 2-lamda ? I mean why the 2nd row

[@stemsupport3645]

I'm assuming you're referring to 1:45 when taking the determinant. I cofactor expanded along the 2nd row, because that row has only one nonzero entry, making the cofactor expansion relatively easy. Check out this video on cofactor expansion if you still have doubts: th-cam.com/video/_75SbA6WKfs/w-d-xo.html

[@priskon5950]

I think you skipped many steps, like I dont understand how we find that x3(-1,0,1) at 9:45

[@justgaming4336]

Exam in 15 min

[@azrmuradl6420]

səviyyəəəə

[@kamilisaintleger8346]

You’re helping me like 2 hours before this exam. 🥹 I’m not religious but you are an angel