Linear Algebra: Ch 3 - Eigenvalues and Eigenvectors (8 of 35) Eigenvector=? of a 3x3 Matrix

[@yugsahu7388]

I think it is important to note that [2 1 1] is not the only solution. Any scalar constant, t, multiplied by the matrix [2 1 1] will be an eigenvector for the eigenvalue given. There are essentially infinite eigenvectors for this eigenvalue and there may be another eigenvectors for another eigenvalue of the matrix. All eigenvectors for a matrix make up the eigenspace.

[@xiu8548]

Great thanks, I learned linear algebra this semester, I can organize well what i have learned until I watch your video. It will be great if you can also explain the vector space section.

[@evaristogabriel8208]

hello, when you say we let x2 and x3 equal to 1, you just chose randomly? they can be any number?

[@manazirahsan1351]

Yeah

[@vuthyyt9977]

They can be other number because X2=X3 so if you put any number it still equal to each other

[@abromchris7670]

I was wondering a year later I still met you on KZbin.

[@sidesmite5739]

Sir, you are if i may a bloody genius! Thank you so much for solving this, I hope you have a great day.

[@andy_phan]

OMG Thanks Michel! Was struggling with this last night, but your video helped me tremendously! Thanks siR! Keep up the content :)

[@swardhamacademy]

Love from India Sir ....Very Easy to understand ....Very Simple Explanation 💓💓❤️❤️

[@MichelvanBiezen]

Welcome to the channel!

[@stevenhamer5826]

need a video on row reduction !!!

[@aleksandric8948]

Dude I got a differential equations exam thursday and you're plugging king

[@MichelvanBiezen]

Glad you found our videos. Good luck on your exam.

[@sitisarah4062]

I’m crying too lot because can’t solve the equation until I found your video! Thank you

[@MichelvanBiezen]

Glad it helped!

[@perinomichael6821]

wow! you are really amazing, + i like your accent thou, sound like Gru (despicable me)

[@MichelvanBiezen]

You're not the first person to say that.

[@perinomichael6821]

ahaha..... thanks for the lecture thou. i hope u have some videos on complex analysis

[@tinomac8790]

kkk seriously thts funny

[@user-wf5rw2hf6s]

@@MichelvanBiezen helloo doctor thank you for these wonderful video . But need help in the equation

[@user-wf5rw2hf6s]

@@MichelvanBiezen find matrix A and B from matrices AB 2×2 and BA 2×2 and its not equal

[@ahmeda.sharrad8360]

u r an amazing teacher sir..big greeting from iraq

[@MichelvanBiezen]

Welcome to the channel!

[@afonsomendes92]

One thing here. First you said we need to reduce the matrix to Reduced Echelon form, then you just did Echelon form which is different than reduced echelon, the latter being an identity matrix. I was doing this reducing to reduced echelon form and ended up with x=0, y=0, z=0 so something was wrong. Then I noticed u say reduced echelon form but just do echelon form. That way u get decent equations which then u can let variable be whatever nunber u choose. my 2 cents. Thanks for the video, i got it finally!

[@qimishibli4488]

I thought I was the only realized about that, thanks for making it clear for me.

[@vkoptchev]

I think it was necessary to stress that we always expect a redundant row in this case, by construction of the matrix A-λI, where λ is an eigenvalue.

[@EagleLogic]

Are there technically an infinite number of eigenvectors that correspond to an eigenvalue in a vector space? Because you could set x2 and x3 to whatever you want as long as they’re equal and that will change x1 and thus the eigenvector. But I believe you’d only have one normalized eigenvector per eigenvalue. Just a thought I had. Thanks for the video professor!

[@victorserras]

What you are talking about is defined as "eigenspace". Basically if v if some eigenvector and k is an arbitrary constant, k*v is the eigenspace of the eigenvector.

[@EagleLogic]

Thanks for clearing this up, Victor! Cheers!

[@John-lf3xf]

Victor Serra So the eigenvector is what? The basis vector of the eigen space?

[@gauthamkrishna6981]

Great work sir.....

[@swardhamacademy]

Sir, can we use the Relation ,AX =lemda X to Finding the eigen Vector .....

[@MichelvanBiezen]

Try it and see what happens.

[@muzzammilmia8060]

Can you not use the trace in order to find the eigenvalues for a 3*3 matrix ?

[@perinomichael6821]

hello sir.please would you help me with this problem here: assuming i have eigenvalues -2, 1, 2; are the eigenvectors of -2 equals to the eigenvectors of 2 with their signs flipped over

[@tinyasira6132]

how can we do this with determinat method istead RRF?

[@MichelvanBiezen]

We have a whole playlist on determinants starting with this video: Linear Algebra: Ch 2 - Determinants (1 of 48) What is a Determinant? (Part 1) kzbin.info/www/bejne/fqLKkmaPl9uDgbc

[@munirtube4230]

great explanation! thank you sir

[@MichelvanBiezen]

Glad it was helpful!

[@ianopindi8491]

Thanks,, from Kenya

[@MichelvanBiezen]

Welcome to the channel!

[@anandnishant77]

Wow it's great you explained. ...for beginners...

[@Desidarius_Erasmus99]

Dear sir I am from India , a private Math tutor . I loved your teaching . But I have a confusion here . Why didn't you use Cayley-Hamilton theorem and characteristics equation here ? And secondly did you take (0 0 0)/null vector as augmented matrix here ? Please reply !!

[@rutusayswhat]

Prof. Michel, why did we neglect the negative root of c at the end? If we do consider it, does that mean we'll be getting two Eigen vectors each with signs flipped over?

[@sherinaoctaviani1610]

Omaigat, thank you so much . So clear, very helpful

[@MichelvanBiezen]

Glad it was helpful!

[@dannggg]

I just found out you do linear algebra too!!! thank god for this i got a final on tuesday!!!!

[@dylanmachado8692]

Thank you very much for the clear explanation

[@SahibzadaInstitute]

sir crimmer rolls are allowed are not?

[@lakshanravindu5846]

Sir ,how to get x1=1 and x2 =1 🤔 i cant understand

[@MichelvanBiezen]

Since we don't have enough information to find the values of x1 and x2 explicitly, we assume a value for x2 (let x2 = 1) and then we calculate the other 2 in terms of that value. We are then able to find the values of each relative to the other and then when we normalize them we find the values of each relative to the normalized value of 1.

[@turuus5215]

Hello, Michel. Can you teach us how to calculate eigen values for NxN matrices?

[@MichelvanBiezen]

When we expand the playlists on linear algebra, we will look into doing so, Currently we are working on a number of other topics.

[@maxwellringirai1640]

well explained..thanks a lot

[@MichelvanBiezen]

Thank you. Glad you liked it. 🙂

[@aryaanr7032]

Thanks a lot sir ...love from india

[@MichelvanBiezen]

Welcome to the channel

[@a.georgopoulou]

Thank you 🙏

[@MichelvanBiezen]

You are welcome.

[@tahirnawaz5989]

Thanks a lot man, very helpful,,.

[@MichelvanBiezen]

Glad you found our videos 🙂

[@hj4820]

Thank you!

[@MichelvanBiezen]

You're welcome! 🙂

[@ragohades6848]

Thanks a lot prof.

[@MichelvanBiezen]

Glad is was helpful

[@rustamshahverdiyev4164]

Hello professor, the lecture is great, i just wonder when the lectures on vector spaces will be ready? Thanks before.

[@scottwitoff8932]

Why did you let x2 and x3 equal 1?

[@saramotamaralayefaemmanuel9772]

Why didn't u make the -1 on the 3rd row on the second coloum equal to 0

[@MichelvanBiezen]

Notice that the second row and the third row look identical. That means we cannot find the exact solution for each of the 3 variables, which means that we must find one variable in terms of the other.

[@saramotamaralayefaemmanuel9772]

@@MichelvanBiezen okay thanks sir

[@aussie3851]

Thankyou! Great video

[@mikiyasshumu8437]

excellent

[@MichelvanBiezen]

Thank you.

[@bilalibrahim2210]

Thank you

[@MichelvanBiezen]

You're welcome

[@zochhuana9556]

Thanks Mr😭😭

[@EMRANKHERALA-cb3ti]

Thank you l.

[@MichelvanBiezen]

You're welcome

[@oserefuareokojie577]

I don't know how long it will take for my comment to be replied but which method did he use to solve the matrix, I've never seen it before

[@MichelvanBiezen]

I used the row echelon form (also called the reduced row echelon form) to solve the matrix. We have a number of examples on the channel that show how to use that form PRECALCULUS 12 - MATRICES

[@paschalcharles7861]

Why you have to let x2=1

[@MichelvanBiezen]

You can let X2 be any value and then find the other variables in terms of X2. But 1 is an easy value to work with so we choose 1.

[@Siam2233]

So clear thanks

[@mary._.2859]

thank you!

[@MichelvanBiezen]

Welcome!

[@benigarcia8218]

thanks! easy to understand for fresh student likes me in college covid-19 :D

[@MichelvanBiezen]

Happy to help!

[@Kyle-gj2lb]

Thanks

[@MichelvanBiezen]

Welcome

[@KF-cg6ey]

thank you so much sir.from afghanistan

[@MichelvanBiezen]

Welcome to the channel!

[@lance4274]

afghan has access to utube? this is from china

[@chimeanhav1439]

Thank you so much!

[@MichelvanBiezen]

You're welcome!

[@edikechristian6158]

Thank you gru

[@MichelvanBiezen]

Thank you 🙂😂😂

[@salmaabobakr1406]

many thanks, you are great.

[@benedictacheampong1290]

video isnt clear

[@sedakun6194]

thank you so much!!!!!!!!!!!!!!!!!!!!!!!!

[@ujolmaharjan2010]

thanks

[@abdulhalimaslanacier3847]

anything you do not know about lectures prof. :)?

[@bodhisattabhattacharjee3338]

Your handwriting is soo perfect, I can't even write so good in a notebook

[@MichelvanBiezen]

Thank you

[@wankmaster69]

Good job

[@robinsonchukwu7295]

I love you so much ❤️❤️❤️

[@MichelvanBiezen]

Thank you. Glad the videos are helpful.

[@johnmanaa1750]

thank you Sir

[@tatendamazadza8319]

NYC bro

[@MichelvanBiezen]

Thanks 🤗

[@eindorito1605]

Mantul om

[@Bioooo]

Vah bapu

[@emeldahdaka4592]

отлично!

[@supunshalitha3638]

good

[@sahilsheikh1712]

Me watching during online exam

[@MichelvanBiezen]

We hope your exam went well.

[@afreenyousaf9438]

Thanks From PAkistan :) We are peace Lovers.. :)

[@MichelvanBiezen]

Welcome to the channel.

[@afreenyousaf4933]

@@MichelvanBiezen ❤️❤️❤️

[@erfanta7398]

ezpz ty man

[@Faizanali-dr5wd]

Good explanation though!! But I would like to suggest that never show your back to students... I mean don't completely turn towards board.... Always eye contact with students ..

[@ashutoshtripathy4948]

Buddha topaa de raha hai vailog