Laplace expansion for computing determinants | Lecture 29 | Matrix Algebra for Engineers

How to compute a determinant using the Laplace expansion (cofactor expansion, expansion by minors).
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[@ProfJeffreyChasnov]

Find other Matrix Algebra videos in my playlist ruclips.net/p/PLkZjai-2Jcxlg-Z1roB0pUwFU-P58tvOx

[@manaynaise]

Thank you very much for this video! I am beginning physics, and was curious about why we would subtract the j-component when solving for the cross product vector. This was a very comprehensible explanation of why.

[@dixshants1227]

how is he even doing the writing? is he writing on glass? Is this some editing genius. also, thank you for that explanation

[@benitomussolini823]

He is writing on glass.
The image is flipped so the writing isn't backwards.

[@nicolasm6845]

@@muhrizqiardi no, he isn't writing backwards, there is a mirror...

[@IStMl]

@@muhrizqiardi bruh

[@scorp6684]

@@nicolasm6845 If there is a mirror then we should see his back, not his front. He is probably just writing in reverse, which is really amazing !

[@robertschumann6977]

@@scorp6684 don't be stupid, watch this to get smarter: ruclips.net/video/eVOPDQ5KYso/видео.html

[@shivangisengar7388]

Thank you so much!!!!! I was so confused about the +, -, + logic.... Your video really helped me... Thanks again sir!!

[@Elias_90]

Actually the +,-,+,- logic can be calculated using the inverse sequence

[@hardikjuneja5348]

(-1)^i+j

[@ebi6097]

I'm more impressed that he's doing this with all those flipped

[@steventhijs6921]

And drawing everything with his left hand as well... stunning

[@onlycheeseextracheese8718]

Have you considered the possibility that he might have just done it normally then inverted the video..? lol

[@flaguser4196]

and in the dark

[@nonentity168]

Thanks a lot, I got confused about the sign logic and this lecture clarified everything.

[@JazzyMiles-il6cy]

Thank you i love you, also like the way you write backwards, really clever

[@electrious_46]

Thanks a lot man, I really appreciate it, you are helping me in Linear Algebra, my prof doesn't explain it in a good way, you're amazing😁

[@Kittyravenhog]

Thank you so much! I'm a Vietnamese student and will have to take calculus mid term exam tomorrow. Now I get the rule 💪💪💪💪❤❤

[@danielakunga8370]

It's really helpful video it makes it easier to understand

[@flaguser4196]

I almost wanted to code it, but the complexity scales by n factorial (in the general case where there might be no zero elements). Wikipedia mentions LU decomposition and Bareiss algorithm as n^3 alternatives.

[@thecaramel-1]

honest to god I didn't understand anything during my lecture in class today about when it came to solving 4x4 matrixes and u have helped greatly thanks!!
p.s do you write in inverse or is there some optical illusion going on with special glass where you can write normally and I also perceive it as normal writing?

[@tdpro3607]

thank you thank you thank you

[@joshuafranzosayta9274]

AMAZING! !!!

[@sanjoymahakur8479]

Thanks

[@hongsethya4932]

Thank god! i find this video ramdomly. because my teacher use across second roll in stead of first, and it's messup my brain because I can't understand why (- + -....) normally we use first roll (+ - +)

[@iris7750]

Thank you.

[@nikshayyadav9472]

hello Sir,
what is there are no zeros in any column?

[@nikshayyadav9472]

then from where we would e able to expand it?

[@yancipan3502]

very clear

[@amankr.kondilya8500]

Thank u sir

[@VitoMusumeci]

OMG! Tom Hanks is way smarter than i thought!

[@tabassumjahansaiky4583]

That's a sneaky little trick

[@willg7103]

how do you get you pen effects in your videos

[@ProfJeffreyChasnov]

ruclips.net/video/WB_CakqElQ0/видео.html

[@girishgarg2816]

Best

[@Carsey-lf5my]

thanks bro

[@catimini-uo1xl]

Much easier to write and visualize columns and rows during operations
a sub1 b sub1 c sub1
a sub2 b sub2 c sub2
a sub3 b sub3 c sub3
Rather than
a b c
d e f
g h i

[@NimaSajeev]

Quiet interesting

[@rohithvemulapally1350]

what if there are no zeros in the 4*4 matrix?

[@ProfJeffreyChasnov]

Then you will have 4! = 24 terms contributing to the determinant.

[@marnotto8269]

@@ProfJeffreyChasnov what? he means what lines you cross

[@marnotto8269]

i understand now what lines to cross, you cross all 3 cofactors
but you only explained for a line with one cofactor and 2 zeros....

[@ryanjackson0x]

@@marnotto8269 It works the same no matter if there are zeros or not. Zero times anything is zero

[@____myocardial_infarction____]

What if there isn't any Zero or any numerical value? What if there is alphabetic values like X,A,B,C?
Please reply sir.

[@ProfJeffreyChasnov]

Then it becomes algebraic.

[@____myocardial_infarction____]

@@ProfJeffreyChasnov but how do I solve that?

[@ProfJeffreyChasnov]

@@____myocardial_infarction____ The determinant becomes an algebraic expression with X, A, B, C, etc. I don't know what you are trying to solve.

[@ryanjackson0x]

@@____myocardial_infarction____ if you are looking for the determinant then you will wind up with det(A) = f, where f is the formula. The more coefficients you know, the more you can solve for the determinant (reduce the equation of f)

[@Bananaaa97]

I he writing on inversely on the whiteboard, whoa

[@ProfJeffreyChasnov]

ruclips.net/video/WB_CakqElQ0/видео.html

[@vor946]

this board is cool as fuck

[@davidlancaster5804]

Waltah....

[@khachikastoyan2221]

Thanks Jeff Bezos

[@souravagarwal5209]

5-3 is 8??? WTf

[@andrewmackay9494]

it is 5 -(-3), so same as saying 5+3

[@linhnguyenvu4241]

I think we much thank you not you jeffrey Chasnos

[@samsting2214]

this shit is not Laplace expansion

[@pmmeurcatpics]

elaborate

[@princeyibby1238]

I agree. It’s not a very rigorous explanation anyways. There’s a lot going on here that is glossed over with “you just need to remember that…”