a beautiful determinant derivation

[@determinantmatrix9584]

Thx for the shoutout Dr Peyam

[@drpeyam]

Loïc!!!!! 😃

[@dk7472]

Bruh that pfp

[@mastershooter64]

I love the fact that he says "thanks for watching" at the start of the video

[@MrCigarro50]

Genial, preciosa y precisa demostración. Gracias por su excelente video.

[@bronkolie]

I figured it out by myself at around 3:36. All the other videos never really explained how the formula they got actually correlated to to the area of a parallelogram. When I tried to derive it on my own I ended up trying to use trigonometry and Pythagoras, to little success. Thanks for the explanation!

[@agustinsaenzanile1900]

So nice that the matematics is after the notation, beautiful

[@FlydingVent9296]

Great video, i wanna see something like this for 3x3 matrices

[@kee2413]

Thanks a lot for your video that make determinant (mathematics)became more visual!

[@mohammedal-haddad2652]

Geometry-based proofs are my favorite. Thank you very much.

[@route66math77]

Very nice, an absolute classic!

[@andrewthompson9446]

That’s was quite beautiful air! Thanks for showing that :)

[@friedrichfreigeist3292]

Lustig, dass ich sowas schon in der Realschule machen durfte. Dabei kommt Lineare Algebra erst in der Uni richtig dran. Nur damals konnte man eben nichts vonwegen Vektorräume und so machen. Man hat die Determinantenformel lediglich benutzt.

[@arnavtete7793]

True true

[@MrRyanroberson1]

funny enough 6:00 this follows into vector mathematics! if you label point (a,b) = A and point (c,d) = B, then you have reinvented the formula for the signed area of the parallelogram spanned by two arbitrary vectors, AxB. and this works in general for any lines since you would first shift the bottom-left vertex to the origin before doing this calculation

[@brendanlawlor2214]

wot a beauty . geometric determinant didn't know it's geometric origin..... thanks Doc !! 😀

[@brendanlawlor2214]

thanks Doc see also my comment on your sec^2 integral with famous similar sec integration by Barrow , Newton's tutor so that Newton didn't invent calculus

[@nicepajuju3900]

Wow that was nice‌!!

[@atahualpaarias1840]

Cool demonstration and funny jokes, thanks!

[@Byc845]

That's really cool!

[@user-wu8yq1rb9t]

Hello Dear Dr Peyam It was so cool, thank you for sharing this with us.

[@manoharsuthar4675]

👍🏻Sir, excellent method .

[@candychiuad]

How does this tie to the determinant?

[@theproofessayist8441]

This is sweet.

[@ekueh]

Wonderful!

[@chessematics]

Back to classroom!!!

[@rarebeeph1783]

so if you have a 2x2 matrix containing a, b, c, and d, then the determinant is just the area of any parallelogram with vertices at (0,0), (a,b), and (c,d)?

[@drpeyam]

Yes, except it’s a signed area

[@nidalapisme]

beautiful! ❤️

[@huwpickrell1209]

Super cool 😎

[@rigoluna1491]

Nice video as always. Could this method be used to find the determinant of a 3x3 and or a 4x4?

[@drpeyam]

It would be harder since the 3x3 determinant has addition and subtraction

[@رضامزوز-خ8ض]

Sir, I heard that if we take a square whose side length is 1 and start dividing it, then the two sides are calculated, then I find the result of 2, but when I reach infinity I find √2

[@رضامزوز-خ8ض]

Which means that 1=√2😕

[@two697]

What?

[@calendar6526]

Ah yes, nowadays, whenever I see a triangle and a parallelogram in the same parallels like that, I always refer to the Euclid's elements book 1 proposition 41 (if I'm not mistaken) about the matters.

[@Leeanne750]

Interesting

[@jabahalder7493]

Linear lalgebra

[@ChristopherEvenstar]

So good

[@faizs9676]

WoW !!!!!!

[@theamazingworldofgusball1852]

Is there some proof of formula for n×n matrix determinant?

[@Batu135]

You mean Laplace Expansion?

[@chessematics]

Nice one. Although each one is nice.

[@antoniocampos9721]

Good !!!

[@eduardvalentin830]

can this be proven using the cross product?( |axb| )

[@Whoeveriam226]

That would involve circular reasoning. Computation of ×prod by det is derived from the fact det gives area

[@yoavlavy2243]

@@d.l.7416 it can be visualized with Cavalieri's theorem, which I think is very intuitive.

[@yoavlavy2243]

@@Whoeveriam226 It is circular only if presented as you said, with the cross product deriving from determinant. That's how I've seen most sources go, like 3b1b's eola series. I think a much better way is to start with the cross product for vectors and then the determinant for matrices

[@tgx3529]

Cool!

[@johnnisshansen]

you jumped over some details,

[@drpeyam]

What?

[@johnnisshansen]

@@drpeyam you have 2 parts of a triangle and claim they add up to half of a rectangle. You should explain why