Minors and Cofactors of a Matrix | Linear Algebra

We go over how to find the minors of a matrix and how to find the cofactors of a matrix. The minor of an entry aij is the determinant of the submatrix when row i and column j are deleted. The cofactor of an entry aij is the minor Mij multiplied by (-1)^(i+j). We go over several examples of finding minors and cofactors of 2x2 matrices, we also find the minors and cofactors of a 3x3 matrix using the cofactor expansion of the determinant. #linearalgebra
Cofactor Expansion Definition of the Determinant: • The Cofactor Definitio...
Linear Algebra course: • Linear Algebra
Linear Algebra exercises: • Linear Algebra Exercises
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[@WrathofMath]

Help me produce this course by joining Wrath of Math to access exclusive and early linear algebra videos, plus lecture notes at the premium tier! kzbin.info/door/yEKvaxi8mt9FMc62MHcliwjoin Linear Algebra course: kzbin.info/aero/PLztBpqftvzxWT5z53AxSqkSaWDhAeToDG Linear Algebra exercises: kzbin.info/aero/PLztBpqftvzxVmiiFW7KtPwBpnHNkTVeJc

[@pipertripp]

The idea of the determinant is amazing. The computation... not so much. But it's good to go through it and learn the terminology and how it works.

[@djdanzo206]

subscribing to this channel was the best decision i ever made

[@WrathofMath]

Appreciate that! Hope you continue to find the videos helpful!

[@PunmasterSTP]

What was the second-best decision you ever made?

[@김테디-t7t]

I love this linear algebra series! the process and the pronunciation is perfect to understand

[@WrathofMath]

Thank you! I'm working very hard to finish the series before summer is over!

[@김테디-t7t]

@@WrathofMath I am looking forward it!

[@aliix8215]

ur channel is a blessing thank u so much

[@WrathofMath]

Glad to help, thanks for watching!

[@cluczar]

best explaining on youtube

[@WrathofMath]

Thank you!

[@felipevillanueva4683]

your videos are amazing. please keep posting

[@spacemanmaths]

so clear thx you

[@danielsoliz9544]

Please keep uploading these videos are amazing

[@WrathofMath]

Thank you, I will!

[@JamesMunene-k5c]

On the last equation when evaluating four rows and columns could you explain where you accuse the ones in brackets (2-18)

[@fungusCH]

thanks big man

[@TrevorLiyao]

Nicely done

[@WrathofMath]

Thanks!

[@lesedimabula7536]

Wow, the last question did puzzled realllyyy my mind😅

[@azarakhshsawmen127]

“We’re going to go over minors”

[@user-wr4yl7tx3w]

For the last example, could you have chosen the second column?

[@WrathofMath]

Certainly! Any row or column will yield the same result.

[@PunmasterSTP]

Cofactor expansion? More like "Crazy; you're on a mission!"

[@mcdemy]

tryna strick a chord and its prolly a minorrrrrrrrrrrrrrrr

[@mcdemy]

thank you for the explanation helped alot

[@krasimirronkov17]

I dont understand how are you calculating determinanta without even defining what they are. And also cofactoring is not the true definition of the determinant

[@WrathofMath]

I said that we are calculating it using the cofactor expansion, so I'm not sure what the question is.

[@krasimirronkov17]

@@WrathofMath the determinant is the sum over all permutations of the numbers from one to n where each summand is the product of -1 to the power of the number of inversions in the permutations times a_1j . a_2j . .. a_nj where you substitute for j consecutively the values of the permutation from 1 to n

[@WrathofMath]

Yes, it is

[@krasimirronkov17]

@@WrathofMath yeah and my idea was that you first talk about cofactoring which is derived from the basic definition is the same as talking about the monotone convergence theorem without talking about limits that was my point. I dont want to crticize you i know it is hard to make yourube videos its just that almost nobody talks about the trie definition of the determinant

[@WrathofMath]

No I get you, I just had time to make this video so I made this one - haven’t had time for a thorough determinants video yet. When I do get to it, it will precede this one in the playlist - but i don’t create the videos in their final ordering as sometimes I have time for Video 4 but not Video 1, so to speak. I also create each video with two audiences in mind: the one who is watching my playlist, and the one who has found the video through search, which also has an effect on how each topic is presented.