Example of 3x3 Eigenvalues and Eigenvectors

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

[bmariani]

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

[Psygression]

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) <factor out the (2-h)
(2-h)[h^2 - 22h + 31 -10]
(2-h)[h^2 - 22h +21] = 0

(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

[hafsamahbub]

You literally saved me before my engineering mathematics quiz

[TheHdz]

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

[rockdread]

Thanks DrBrainWalton, many thumbs up for explanation !

[isaacbrown]

Great video. Learned it in 15 mins with your help

[WateryIce]

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

[RaghiPandit]

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

[indumathi]

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

[kumailkhaki]

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

[RyzenGamerZ]

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

[davidthaler]

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?

[kwakyedanielegyire]

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

[ssebitaabawamala]

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

[rinnie]

its very clear explaination for beginners.Thank you.

[josephang]

Thanks! You really helped me understand my tutorial

[Reginescbeiibii]

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

[vuyiswanjoko]

Thank very much for making this topic easy to understand

[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.

[samfitzpatrick]

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