Example of 3x3 Eigenvalues and Eigenvectors

Illustrate the process of finding eigenvalues and corresponding eigenvectors of a 3x3 matrix.

[@bmariani52]

Finally a clear concise step by step showing the details of how to solve the matrix using lamda to produce eigenvalue and eigenvector.

[@hafsamahbub]

You literally saved me before my engineering mathematics quiz

[@Psygression91]

Simpler way to factorize - Instead of expanding the brackets to get a polynomial to the 3rd power you could just leave the quadratic and manipulate the other terms to get (let h = lambda): (2-h)[h^2 - 22h + 40 - 9] - 11 + h + 9 - 18 +9h (2-h)[h^2 - 22h + 40 - 9] + 10h - 20 < manipluate this term (2-h)[h^2 - 22h + 31] - (20 - 10h) (2-h)[h^2 - 22h + 31] - 10 (2-h) h = 2 [h^2 - 22h + 21] can be solved using the quadratic formula [B+- squaroot (b^2 - 4ac)]/2 This leaves you with: h=[22+20]/2 & [22-20]/2 which gives you h = 21 & 1

[@michaeletta4849]

Thanks for this quick hint.

[@funnyfootballworld906]

You are a live saver bro 🙏🙏🙏

[@collinsokonkwor2918]

This video is a saving grace!

[@isaacbrown2248]

Great video. Learned it in 15 mins with your help

[@rockdread3415]

Thanks DrBrainWalton, many thumbs up for explanation !

[@indumathi5182]

So clarity in your explanation. No words to praise you. Thank you. ..please keep doing on other topics

[@mbisetakobana]

work of a genius!

[@RaghiPandit]

Thanks a lot for such a detailed explanation of the problem!! Thanks for every step.. cheers :D

[@Alif1111111]

+Raghi Pandit can i add u in insta??

[@TheHdz2011]

BECAUSE OF THIS MAN, I EXCELLED ON MY EC QUIZ AND GOT TO OPT OUT OF MY FINAL!!!

[@nanayawberko3212]

K

[@WateryIce54321]

Thank you for your straightforward approach. My god I lost count of the number of explanations that over complicate this.

[@RyzenGamerZ]

after 6 years, still this video is useful thanks a lot

[@jamesdean4542]

At 3:20 why is the co-factor -1???

[@josephang1513]

Thanks! You really helped me understand my tutorial

[@kwakyedanielegyire5003]

The explanation is very great it has really given me deep understanding

[@samfitzpatrick1866]

How do i find the eigenvector if when I reduce the nullspace I get the vector [100, 010, 001] instead of [100,010,000]?

[@saminfarhan6140]

you deserve a nobel...

[@jurianfct]

w h Y

[@Reginesc520beiibii]

thank you very much sir, i finally can catch up with my classTT

[@rinnie897]

its very clear explaination for beginners.Thank you.

[@davidthaler7018]

Very easy to understand, but…you get the roots from looking at a graph you can’t generate during an exam so I’m guessing the graph/ intercepts will be provided?

[@snowcuddler4691]

In getting eigenvector in each eigenvalues, can i use gaussian-elimination??

[@MahmoudSalahkhalifa]

so good and excellent thanks Dr

[@JL0419ful]

I don't understand why when eigenvalue=21, the eigenvector needs to multipled by 6. Is it a must for the eigenvector to be integers?

[@mehrosenasir3966]

why did you subtract the (3R2-R1) in the end, do we really need to do the last step?,however we have already fulfill the conditions of an echelon form, I guess

[@Memes_uploader]

I get -lambda^3 + 4lambda^2 - lambda - 18 (this is another example from the book) and it does not crosses with x, what should I do

[@shahzaibhayatkhan]

Perfectly explained :) Thank you bro.

[@jurianfct]

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[@nicholasmathiassen6188]

Why do we need to change the cofactor to negative when you add the number "1" at 3:28 min into the video? I don't understand why we need to multiply with a number, in this situation we multiply with (-1).

[@sergebyusajabo2138]

It's helpful and understandable. Thanks

[@vuyiswanjoko6029]

Thank very much for making this topic easy to understand

[@shahsudip2005]

how are you finding the elements of matrix as free and not free in which condition are you multiply wuth x,y,z

[@mehroofayazz8720]

i have one confusion ain't homogeneous system of equation solved by echelon form ? where on the basis of rank it gives us the solution.

[@ssebitaabawamala6861]

Thank you..I had no idea what was going before I saw video.

[@jurianfct]

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[@r4ndomboy]

At 9:19, how does the graph not go to minus infinity? EDIT NM I figured it out, it crosses the X axis again at 21 and goes to minus infinity.

[@kumailkhaki266]

I liked this before watching it, it better be good!

[@jurianfct]

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[@nisalisadara6449]

THANK YOU SO MUCH. I am finally capable of doing this right cuz our prof could only send hand written notes for the lesson due these horrible covid hazard. Plus we didn't have online lectures. So thx again

[@EagleLogic]

Damn this is a huge process

[@MSTK-qp4uz]

Thanks again for your effort....

[@Mohamad32010171]

thank you very much sir .. ^_^ you r a life saver ..

[@jakiiechacon]

GREAT EXPLANATION. THANK YOU (:

[@jurianfct]

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[@SyznNzm]

why do you swap row2 and row3? do we need to let row3=0?

[@MrIshmael456]

I don't know if this is helpful still, but he did it because a row that is all zeros has to be at the bottom of the matrix. I believe it is an issue about ordering the matrix when you have a row of zeros.

[@DrBrainWalton]

To solve the system of equations, swapping rows is not necessary. To find the row equivalent matrix that is in echelon form, all rows of zero need to be at the bottom of the matrix.

[@joris7000]

Excellent video thanks alot!

[@jurianfct]

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[@Spix_Weltschmerz-Pucket]

Thank you!

[@asheshsrivastava8921]

It was great help!!!

[@KingDuken]

I usually leave the (2-x) out so I can get a quadratic in the middle so I can factor later to find the roots.

[@surveygeomatics]

thanks ooh this helps me alot God bless you

[@noontanklangdon1475]

Thank you so much. :)

[@archenemy_1]

thank you for this

[@prasannanivas4575]

thanks a looooooottttt man..... hats off may god bless ;u

[@mehrabfatima3693]

could you please explain (80-44+2lamda^2) how did you get this?

[@williamchilimbo1137]

Mehrab Fatima yuko vizur

[@Tims20]

How to know which variable is free?

[@ravinderreddy9723]

Great explanation

[@jurianfct]

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[@Diamond_Hanz]

love the video... i'm shocked that i got the answer right !

[@MSTK-qp4uz]

Thanks..that was very helpful..but I wanna say that you would have used the remainder theorem and the factor theorem by picking a value that makes the polynomial =0..then you will have one factor and the other two you can easily find them since you got a quadratic equation..

[@pnwtutoring]

Look at the coefficient of each term , the sum of them be equal to zero, so the first solution of this equation = 1.

[@sirzahid6168]

VERY EXUISITE METHOD

[@Planes4Days]

Can someone explain to me how 3 times 3 became -9?

[@maheenhashmi7680]

Can u plz do this question without the calculator?

[@MrRobertthereau]

+Maheen Hashmi You just have to test the value of the polynomial function for every integer root + or - 1,2,3,5,7,14,21,42 (you have to test them until you find 3 roots because a polynomial has n roots, where n is the degree of the polynomial). It is simple but it will take time. If you find a root, you can divide the original polynomial by x - root and continue finding roots for the "new polynomial"

[@muhammadjawad8401]

Maheen Hashmi, Its very simple you just apply the factor theorem on that equation (polynomial of degree 3 equation), After that you will get a factor of that then divide the equation with that factor, so you will get a polynomial of degree 2. then simply factorize, that's all I hope you understand.

[@jctop10s29]

but 4 can also be an answer

[@bmariani52]

All I need now is a method to create the cubic equation of lamdas in a programing routine.

[@alidener]

thank you so much..

[@jurianfct]

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[@kumailkhaki266]

It was good! Very good!

[@jurianfct]

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[@marklaurente4823]

It's very clear. Thank you for making this video Sir.

[@mehmetdogan8422]

perfect

[@atiqulislamp.eng.4211]

Thanks Sujoy

[@FuriouGladiator]

preach!!!

[@ryancoughlin2192]

this shit was money

[@jurianfct]

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[@asnsr3573]

Why didnt we say the z is free when we were solving for lamda=1 ? :/

[@steffandall5785]

i know, right? it must have been.

[@robbymashegorobby9310]

thanks.

[@albraamagdi7864]

very nice

[@basitnazir9218]

Good

[@maheenhashmi7680]

I m having a trouble in solving step 2

[@laiaplaiap1688]

👍

[@johnwayne7923]

holly shit its so easy thank u so much

[@Eli7PM]

if you multiplied the vector X*a, "a" a scalar equal to 6, shouldn't you multiply the original matrix by that scalar also? a*L*A=a*L*X=L(a*A)=L(a*X) *=multiplication a=scalar L=lamda eigenvalue A=original matrix X=eigenvector

[@tracysibanda868]

Is it A_lambda or lambda _A

[@limonkhan9740]

thanx

[@herodiada8574]

Thaaaaaaanks

[@SADRACFIRMINO]

will Z be allways the free value?????

[@balasubramanianarumugam1218]

nice

[@jurianfct]

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[@dexter12x70]

this is another faster method and easy method ...try this ...............lambda cube+ (lambda square)sum of the diagnols (2+2+20)+(lambda)sum of coefficient of diagnols+determinant=0

[@NORMAL_GUY_69]

hell no u teaching we guys the incorrect .. u got my mind cleared and i forgot whatever i had learned till date about maths ,,lol ,,so many errors..seriously

[@hassanalrehamy5379]

+Utkrisht Sharma you are so dumb

[@NORMAL_GUY_69]

+hassan alrehamy WTF shut your hole ,, pisssing oveeer myyy post

[@hisxmark]

The explanation was good, but the scrawl was nearly illegible.

[@Daver2212]

I have never been able to factorise.

[@stevenhamer5826]

good video but wish would stop jumping steps

[@hocinemansouri5978]

i guess there is a mistake when you calculate the det in 3rd row you should do 3(1st row((2-y)(1)) 2nd row((1)(2-y))

[@MuhammadFaiz-sb9kx]

7:20 .....how come 80-18-20-9+9-18= 42?????

[@deepchetry2]

I have a confused in last step

[@mauricioalexandermartinezq1549]

I think that he made a mistake in finding the determinants because it is -1 if it is because of, when finding the determinants

[@Muxik4k]

Can my eigen vector be 0, 0, 0?

[@syedtalhaiftikhar2754]

I believe that it would not be considered an eigenvector because it is a trivial solution to (A-lamda*I)x=0

[@kaayaharuna6307]

@ Dr brain Walton,I totally doubt u here,ur wrong

[@jonida9927]

now instead of just doing it explain the steps we are watching the video to learn not to see if you can solve it or not

[@johnchang8279]

Too long. You can quickly notice that one eigenvalue is 1. The the trace = 24, so the other λ's add to 23. The determinant, after R3-R1-R2, is 14*(4-1)=42, so their product is 42. That gives 2 and 21.

[@AhmedSK143]

that lamda calculation is so long and boring

[@irregulargamer1352]

nice explanation, crappy writing.

[@ubongbassey2206]

Thank you!