Determinants

[@mauriciobarda]

doing column operations is ok because is like doing row operations on the transpose, so the determinant is the same for the right operations.

[@henrymiller5709]

For matrix A, directly separate it into two matrices, one includes only x and 0 terms, another one contains only y and 0 terms. And the result is x^5+y^5

[@aditya-bl5xh]

For B you can take sum of all rows in row 1 and then take it out, so you'll be left with first row being all 1. And then using this to remove all remaining y's.

[@onuryes]

This is a great example but I believe during adding columns there are mistakes. One column addition consecutively is actually enough to get an upper triangular matrix.

[@ΠετροςΜαρκαδας]

When computing the determinant of matrix B and during the first phase (row operations), we could also substitute the first row with row1-row5 (x-y 0 0 0 y-x).This will produce a matrix that is the transpose of matrix A if it had x-y instead of x and y-x instead of y. Therefore the determinant of B is (x-y)^5 + (y-x)^5 which is 0. Could someone please rectify my logic since this is a different result than the one derived in the video. Thank you in advance!

[@vincentfaure4472]

Hi Πετρος Μαρκαδας ,you may not be allowed to do this substitution because otherwise you end up with a singular matrix; keep the first row as a pivot row...hope this can help you.

[@maxim_ml]

same

[@chuanweizhang3164]

although its been 2 years, but somebody later might find it useful. The problem is when we subtract row[i] with row[i-1], we can only get four [x-y 0 0 0 y-x](the 0s are in different index, but you know what i mean). when you want to replace the first row, there is a problem, there is no row to deduct. to get all five [x-y 0 0 0 y-x], you need to subtract row1 with row5, but row 1 are still (x y y y y), row 5 now changed to (0 0 0 y-x x-y), you cant do the same thing to row 1, so you are left with row 1 unchanged. The key is we can subtract rows, but only one row at a time. when we get row2 to row5 straight, row1 have nothing to subtract from. you cant subtract row1 with the original row5.

[@lee_land_y69]

thanks

[@middlevoids]

Well, that was the cool one! Thanks!

[@fruitninja8475]

omg I don't know we can do column exchange

[@elephant5597]

i never knew that you can do column operations

[@red_l6634]

determinant(A)=determinant(A^T). So, you can do it only if you want to calculate the determinant. It's like getting the transpose, do row operations, then transpose the transpose so A^t^t=A and you continue with A, then you can take the transpose again e.t.c.

[@rafaelr5243]

No one has ever said what good a determinant is. I mean what is it used for? How does it help us?

[@John-po5vp]

3b1b's videos will answer your question.

[@tabrisvan1319]

9分钟往后那里，其实把所有列都加到第一列，再按第一列展开，就行了

[@JohnDoe-nr5zi]

when computing determinant using cofactor method we can choose to go either through a column or a row?

[@devonrayramirez3691]

John Doe Yep! A simple way to think about it is through det(At) = det(A) since by using cofactor on A’s column, you’re simply using cofactor on At’s row which would still give the correct answer

[@nprithvi24]

Yeah that seems like a shortcut I would prefer lol. Great video nonetheless.

[@jinyunghong]

I don’t understand the explanation about the matrix A. I could get the correct determinant of A by manually applying elimination steps to it but how can you choose ‘y’ from the 5th row of the matrix to use its cofactor, not the 1st row of it? Is there something I miss?

[@jinyunghong]

I got an idea. You can think the determinant of A is equal to the determinant of A transpose.

[@jasonqian]

I wonder if she, Linan Chen, is a communist party member who deliberately chose to live in a capitalist country. If she is a communist, a phenomenon so common that many students are CCP members in a Chinese key university such as Qinghua, she either has long betrayed the party and totally embraced Western "materialist decadence" or, is still serving as a cog in that system and carries some kind of a special mission. Of course, no matter what is going on in her mind the fact that she married a guilao (鬼佬）and settled down in a free society must mean something.

[@serdarcite]

lol what are you even talking about? Is she really a communist party member or you say so because she is chinese?

[@laytion4585]

what is this crazy comment on this amazing educational video

[@gaconc1]

"There are more smart people in China than any kinds of people in the US" - the social network

[@demonjunkie6588]

you should go outside my friend

[@KraftButFucked]

I am sure everything is possible in world as demonstrated by this comment in Determinants tutorial