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

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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!

patrickmayer

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

renemartinez

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

garthenar

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

more_math

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 YouTube, 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

Nothing-joci

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

HylianEvil

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

KingImmortal

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.

waltke

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

agh

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?

khetagtebiev

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

ektabansal

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

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

Linear Algebra 14TBD: The Linear Property of the Determinant

Linear Algebra 14TBD: An Application of the Product Property of the Determinant

Linear Algebra 14TBD: The Effect of Adding a Multiple of One Row to Another on the Determinant

Linear Algebra 14TBD: The Alternating Property of the Determinant

Linear Algebra 14TBD: Overview of the Properties of the Determinant

Linear Algebra 14TBD: Calculating the 3x3 Determinant the American Way

Linear Algebra 14TBD: The Direct Algebraic Definition of the Determinant

Linear Algebra 14TBD: The Product Property of the Determinant - Proof for Elementary Matrices

Linear Algebra 14TBD: Setting the Stage for the NxN Determinant

Linear Algebra 14TBD: Calculation of Areas and Volumes by the Determinant

Linear Algebra 14TBD: Calculating the 3x3 Determinant the Indian Way

Linear Algebra 14TBD: Calculation of the Determinant by Gaussian Elimination

Linear Algebra 14TBD: The 3x3 Determinant - A 2nd Illustration

Linear Algebra 14TBD: The Transpose Property of the Determinant

Linear Algebra 14TBD: An Elegant Approach to Defining the Determinant

DETERMINANTS when ROWS or COLUMNS REPEAT (or are zero) // Short Lecture // Linear Algebra

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Linear Algebra 14TBD: Interesting 2x2 Determinant Examples

Linear Algebra 14TBD: The Determinant of a Triangular Matrix

Oxford Linear Algebra: The Easiest Method to Calculate Determinants

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Linear Algebra 14TBD: Derivation of the 3x3 Determinant

Determinants can be computed along any row or column - choose the easiest!