❖ Finding Eigenvalues and Eigenvectors : 2 x 2 Matrix Example ❖ 

Please definitely post a 3x3 example! This is super helpful.

Can you generalize discuss the implications of the cases where the eigenvalues come out as imaginary?

How did you found adjoint of 2x2 matrix youre moving very fast at 8:20 finding B matrix? Because its equal to zero matrix please reply fast i have exam two days later

Do we have to follow all these steps or is there a faster way to go about it?

Please take an example of solving 3×3 matrix too

+The Visionary I'm sure I've helped a few here and there :)

you are the only reason I am able to pass calculus and linear algebra. My teachers are great, but for some reason this "one on one" examples are really what gets me to understand it.

Its because he's too the point and writes things in steps, like i was watching some other videos of people explaining this and there just waffling on and jumping between things without explaining them as if the person has done them before. There isn't really much excuse when your doing it by a video because you can prepare the most key and important points and how to say it, before doing the video.

Every time I have written a Linear Algebra and Calculus I & II exams/tests, I always get a, "What did patrickJMT teach me?" moment. I'm probably going to have those brilliant moments for the next 4 years... Then I will come back to this same video and thank you for catapulting me into graduation day with a degree in Mechanical Engineering.

hey where are you studying Mechanical Engineering > .. Im studying it At the University of Guyana

Just did the same with an exam coming up in 2 weeks. Why do we do these things to our self?!?

LMAO!.

@@KH-ft4ut Exactly.. My exam is in just after 2 weeks and I ve started to look at things just now

@@Sam-wt1cx Good luck mate, I passed my exam. But I still have no idea what Eigenvalues or eigenvectors are actually useful for.

The Duke lol I guess I’m lucky my professor is not bad although these videos help me out cuz I’m taking two math classes and I get confused at times.

+Allegro Crab introductory ?Linear algebra?

+Allegro Crab It's currently 1:15am here, my exam is 9am. I can relate :P

HaydenMcM1 you're australian too? good luck m8.

***** Yep, thanks mate :)

its already 2016 but I can relate to what you said. its 2am and I have my exams later at 9am. 😂😂

When they explain this stuff in an hour they just rush through it and don't explain anything, Patrick is a life saver

Eric Da Silva Uni profs are usless bro

i guess thats why there's that saying "those who can, do; those who can't, teach"

Yea seriously if it weren't for patrickjmt and other RU-viders I would have no idea wtf is going on in my diff eq class.

University professors are not there to teach you. They are there to provide you with material that you should already know. University isn't high school.

Literally !

i am already rewarded by feeling appreciated in this world as your comment does for me ;)

Angelo Ungery the best regards and best wishes

+Flambe nah, just a normal guy trying to help in the best way i know how!

+patrickJMT JOHN 8:32 :) #lifeabove

+Flambe I don't think it's right comparing him to god. I mean he's good... but he's no Patrick.

definitely a god among men

Dear Sir, I sincerely thank you for taking the effort to create such useful videos. I was reading through my notes and textbook till i began to panic. I have an exam in 2 days time and I would no have understood this topic if it were not for your kind help. Best regards from Singapore.

也许，这些理论在某些教授的理解能力中，还不是十分清晰的。思路未清，词即难达。 Maybe,some professors have not get the clear understanding in their mind. No one can explain more clearly than he think.

I think that since they have done it so many times, and have realized the importance of the _concept_, they focus so much on the theorem and not on the operation. It is important, but a lots of times you understand the importance and _can use it_ after you are familiar with SEVERAL tools. One day, they just click and understand them better. That's not the situation that students are in, they ask us to remember lots of things that stack upon each other to build new things and they tell us "this (ALL) is important"... well, we (still) not care, we don't have the tools to care either.

Ha, glad you feel that way!

May I ask for an application example for Eigenvectors and Eigenvalues such as Page Rank algorithm?

+HaydenHatTrick same

Lol, I think you mean sadist, my Eigen value were 5.372 and -.372.......

+Cj Looklin Tell your professor to screw off. I feel so sorry for you

lol i had a three decimal eigenvalues. and had to do inverse off a 5x5. not terrible but he wanted adj(5x5)/det(5x5). This means that ill end up having to find the det of 25 4x4 matricies

Oh noooooooooooooooooooooooooooo

Jajaja I couldn't agree more. It's pitiful how many teachers are reluctant to integrating technology to subjects like this

yes any number you can since it just a scalar. For simplicity just pick number 1.

Thanks!

+patrickJMT Hey Patrick. For the first problem with eigenvalue T = 8, you used a row reduction method for finding the vector x. In doing so, you made the second row of the matrix have all zeros...BUT for the second eigenvalue T = -2, you made the first row have all zeros. Can you explain why you used that method and didn't use the same row in both cases?

+JC Tutoring it's the same if you make the second row of the matrix have all zeros, you still have same result

For the eigenvalue -2, I divided the top row by 3 so instead of 9 and 3 on the top, I ended up with 3 and 1. From there you can do Row1-Row2 and get (3,1) on top and (0,0) on bottom row.

Yeah, like you can also use the letter A for example X2= A and X1=3A

I have the exact same question, choosing 1 seemed arbitrary but I do not understand why it was chosen.

@@seansethi196 It ultimately doesn't matter, because you just need one any one eigenvector. Remember, any non-zero scalar multiple of an eigenvector is also an eigenvector for a particular eigenvalue.

@@moatef1886 appreciate the reply, thank you!

It doesn't matter what you set x2= to. you can pick any number you want because any non zero multiple of eigenvector xbar is an eigenvector

I don't like how i explained that... let me do it again. Once you find the relation between x2 and x1 it doesnt matter what numbers you chose. You may pick any x1 to get a corresponding x2.

ah okay, thank you so much I've thought about It but I was uncertain, thank you so much for your answers, and sorry If I make english misspellings, I'm moroccan and we study In french

bob butts Love the explanation. You had it all messed up at first but you came back with the second post and cleared it up. You could have left it all messed up and probably nobody would have noticed but you came back... You came back. God damn you got a bright future. Best of luck in future endeavors and shout out to any who enjoys linear algebra

​@@aussiecomrade5972 There is a subspace of eigenvectors with x1 and x2 corresponding (or relational) entries. (orignal matrix) * (subspace of eigen vectors that you choose from)= (eigenvalue) * (eigenvector chosen).

Sorry for the late reply but it may help others: You pick numbers that reduce the bottom row to zero, here 3*R1 is the same as -R2 so by adding them together they cancel out, giving the desired zero on the bottom row.

Thank you from Australia

Welcome from india

Hey it's been 3 years but yeah.... WTF is row reduction?

@@peterlee5726 In typical University Linear Algebra classes, we have to reduce our matrices manually. This can easily be done in most calculators or something like MATLAB.

Peter Lee I know your comment is old, but RU-vid for his video called “gauss-Jordan elimination” that’s what row reduction is

but why we need row reduction here

Could anybody explain it to me please?

yes i want to know about this too

@@shirashira8871 I'm in the same position hahah I want to know too

@@shirashira8871 got the answer ! you can see in others comments : "ultimately doesn't matter, because you just need one any one eigenvector. Remember, any non-zero scalar multiple of an eigenvector is also an eigenvector for a particular eigenvalue."

@@sauceandalouse2624 Thank you for your explanation:)

I love you baby 😊😍😘😚😗😙

Kind of a comforting sound tbh

Instead of thinking of the problem as: Find THE eigenvector. Reword it to: Find AN eigenvector. When he gets the matrix into Reduced Row Echelon Form, - research this to understand why we row reduce - any real number we plug into the equation he writes at 7:43 for x1 or x2(only pick a number for 1 value and solve for the other) can reduce to {3 1} like he got, so that's why its an arbitrary selection. Try it!

@@supahotfire8886 Thanks. :) I'm out of school now but Ill try it lol. I think i did accomplish this in one of my later courses.

are you an engineer now lol@@AceofDlamonds

@@litjew6669 Hehe...i'll just say I wish I could rewind time and study computer science instead 😂

Can someone answer this plz????

It's a variable, i think he is using the gauss Jordan formula

he is trying to reduce it in echelon form.

I'm assuming ur stuck after you've written down det(A-lambda times I). Go back to your notes on calculating the determinant of a 3x3 matrix. It's just a bunch of tedious calculations at that point, and you end up with a cubic equation which of course is a little more difficult to factor to determine the 3 roots which then give you 3 eigenvalues. Then its just a matter of substitution as Patrick showed you to get the eigenvectors.

Yes, once you find an eigenvector, any scalar multiple of that vector will also be an eigenvector.

more likely a sadist...masochism is self-inflicted pain

I was scrolling just to find a comment like this, lol