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

In this video I will find eigenvector=? given a 3x3 matrix and an eigenvalue.

Next video in this series can be seen at:

[yugsahu]

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.

[xiu]

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.

[sidesmite]

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

[abromchris]

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

[andy_phan]

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

[aleksandric]

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

[sitisarah]

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

[evaristogabriel]

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

[swardhamacademy]

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

[afonsomendes]

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!

[ahmeda.sharrad]

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

[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.

[perinomichael]

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

[dannggg]

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

[sherinaoctaviani]

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

[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!

[anandnishant]

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

[dylanmachado]

Thank you very much for the clear explanation

[muzzammilmia]

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

[tinyasira]

how can we do this with determinat method istead RRF?