Linear Algebra 14TBD: Row or Column Expansion of the Determinant by Cofactors (or Minors)

[@MathTheBeautiful]

Go to LEM.MA/LA for videos, exercises, and to ask us questions directly.

[@patrickmayer9218]

Just FYI for people watching his work at 7:23, it's supposed to be 5 7 3, not 5 8 2. Main takeaway from this video is that determinants by column are calculated exactly like determinants for rows. Thanks for the video!

[@renemartinez3014]

Your videos are so good that I gave you thumbs up even before starting it.

[@MathTheBeautiful]

I did the same to your comment.

[@garthenar]

Very well done. My professor wrote an odd equation on the board but now that I've seen this that equation makes sense.

[@more_math]

Many thanks for making these videos. They are very helpful to me.

[@HylianEvil]

Man, have you lost weight? You're looking good! Thank you for making these videos!

[@UnforsakenXII]

+HylianEvil I was about to say this. Thanks alot professor.

[@Nothing-jo8ci]

Hello Professor Dr. Grinfeld; First I definitely must thank you for your teaching, which is very beautiful and the most appropriate for future mathematicians. As in college as on KZbin, many professors teach an engineering way If I may say, which doesn't include proofs, paths of reasoning and critical thinking. Is more about applications, solving exercises and very connected to the real world. I've already finished Linear Algebra 2 playlist. I've actually learned math for once. Your map of the determinants was just beautiful art and using a laser? Can't describe using other words than elegant, beautiful and logical. Now I would like to learn calculus for now. Do you have any calculus playlist for begginers as the linear algebra ones? I went to lemma, but only found a video about it which isn't you :( Thank you very much

[@marioandres1055]

You are the best!

[@KingImmortal]

Super Awesome, thank you so much!!! Your explanation with the signs helped a lot !!

[@waltke2]

Thank you so much for making these videos. They have been a great help to me, and I imagine to many others. Could I ask you to take a look at the "5 8 2" entry at 7:23 and see if you are happy with it? I expected it to be "5 7 3". In this case, the whole matrix is multiplied by 0 so it doesn't affect the result. I hate to be the nit-picker but I thought you might want to check it out. It is always possible that I misunderstand some aspect of the calculation, of course, and perhaps you got it right all along.

[@MathTheBeautiful]

+A3jose348sf Yes, 573. Thank you, I'll have to delete the video and upload a new edited version.

[@MathTheBeautiful]

+A3jose348sf No worries: CGI.

[@MathTheBeautiful]

+Walter Kennamer Ha! kzbin.info/www/bejne/o5O4fI19o5KcfaM

[@ektabansal5332]

Thanks professor for the playlist... Btw Which song was that??

[@MathTheBeautiful]

kzbin.info/www/bejne/hmXOY3-EhbeJY5I

[@ektabansal5332]

@@MathTheBeautiful thanks a lot Professor

[@khetagtebiev3838]

Thank you Pavel, I am glad I've found you. I've gotten this far from the very beginning of the series in a week or so :) I still can't understand one thing about determinants. Why doesn't it make sense in principle to try and define a determinant for non-square matrices? Have you already explained that anywhere in your videos?

[@MathTheBeautiful]

There are analogous definitions, but none that yields a single number. The determinant is a measure of the change in "volume" under a linear transformation. But if dimensions are mismatched, the comparison doesn't work.

[@danv8718]

That's an awesome song!

[@MathTheBeautiful]

From this movie: kzbin.info/www/bejne/hmXOY3-EhbeJY5I

[@sandilemngqibisa7129]

super cool

[@agh1750]

Can anyone explain why the identity is true? As in why the determinant equals the expansion?

[@MathTheBeautiful]

It follows from the general algebraic definition kzbin.info/www/bejne/emnVmJuhrctnm7euz Think about what is left when you factor out one of the terms.