🔷15 - Eigenvalues and Eigenvectors of a 3x3 Matrix

🔷14 - Eigenvalues and Eigenvectors of a 3x3 Matrix

Given that A is a square matrix (nxn),
Ax = kx -------(1), where
A = an nxn matrix (square matrix),
x = eigenvector of A corresponding to k,
k = eigenvalue of A corresponding to x

It is usually asked to find the eigenvalue as well as the eigenvector that satisfy the above equation.
Notice that we are only interested in the solution with x not equal to zero.
from (1), Ax = kx
Ax = kIx ------(2) ,
(A-kI)x = 0 ----(3)

the system will give a non-zero solution if and only if det (A-kI)x = 0 ,
det (A-kI) gives rise to a polynomial called the characteristic polynomial and the equation formed when det (A-kI) = 0 is called the characteristic equation. The solutions to the equation are the eigenvalues....

Visit channel Playlist for more videos on Engineering mathematics, applied electricity and Basic Mechanics.
Kindly support and Subscribe
Thank you

[evansokosodo]

This is so straightforward. What a good teacher! Many thanks.

[kwabenablessed]

Very clear explanations. This was very helpful. Thank you

[Dee_alh]

you are explaining from the bottom of your heart thank you

[tomasito_]

Your videos on linear algebra have so far been very helpful. I'd love videos on Diagonalisation of matrices, coordinate transformations and Jordan block decompositions. Thanks!

[raghavyadav]

your videos are really helpful for calculus and linear algebra, thank you!!

[AbbSalehi]

I have two original equations with three unknowns ( X, Y, Z). I've just added one extra equation to make the original equations solvable. What should I call this adding process in mathematics? I just need the correct wording for that. Any help would be appreciated. Thanks

[SonnyTechAcademy]

Thanks man. Well explained....the video is long but it's worth it :)

[DD]

Thanks for this. You are explaining directly from your heart, with care and love

[mrseis]

Hey buddy, I want to thank you for taking on a matrix without 0's because most of these youtube videos i've come across have 0's at the top or bottom and its annoying because the problem i'm tryin to solve is anything but 0's! Thanks!

[Salamanca-joro]

Absolute cinema! i have final exam on Tuesday and you just saved me

[danielkadima]

with another 3x3 matrix I found the characteristic polynomial, I put the equation which was cubic into the calculator. This way is still difficult to find the eigen values unless I am doing this wrong. So I took the same equation and plugged it into Mathway I found that the roots are decimals?

[sajjalsayjal]

How we find these eigen values that you write??

[petrkasanda]

Thanks very much for this teaching
Much love ❤ and respect from zambia 🇿🇲🇿🇲🇿🇲

[palmershot]

I've got a test today and this is all. I needed

[calvinbasotho]

Hi. I need to know how you simplified that cubid equation to find 3 lambda values

[alexkim]

Wow thanks for the clear explanation! Can I understand why when you interchange the rows in matrix, it doesn't change the final result?

[yahyadiaa]

You saved me from failing my exam for the 4th time

[masked_man]

Explanation is very good and clear. Keep it up.

[edsonsimbaya]

Thanks, this is very simple explanation

[NeverTHOUGHTofIT]

Can you do a video about Eugene roots of symmetric matrix that would be good