That feeling when you realize you’re watching a math tutorial to fall asleep easier 😅 Nice example 👍
@mokopa
4 жыл бұрын
I do the same! I watch it twice, then go to bed, trying to remember as much as I can and do the math in my head while I'm drifting off. So much better than enumerating sheep.
@ramanunnikrishnan7354
4 жыл бұрын
how can you sleep after that, it gets me so excited that sometimes my sleep gets lost
@satishchaudhary7978
4 жыл бұрын
@@ramanunnikrishnan7354 same happens with me
@matteo23battini
4 жыл бұрын
The matrix at 4:25 is the Vandermonde matrix. It has some curious facts for example the determinant it's equal to the product of (aj-ai) with 1
@SimonClarkstone
4 жыл бұрын
I never learnt these properties of the determinant formally, but they are amusingly clearly true if you consider how the determinant is the (signed) volume of a parallelepiped whose 12 edges are 4 copies of the 3 line segments given as the 3 columns of the matrix. Thanks to the channel 3 Blue 1 Brown for teaching me that.
@drsonaligupta75
4 жыл бұрын
I have another solution: We know that if a homogeneous system of linear equation has non zero solution then the determinant Of the coefficients is zero ( cramer's rule) So lets consider the system of linear equations t(x) + t^2 (y) + (1+t^3)z=0 For t= a,b,c (Like replace t by a , b, c we will get three linear equations of variables x,y,z) We want to find the condition on a,b,c given that the system of linear equation has a non zero solution ( a solution other than x=y=z=0) Which can be rephrased as: The cubic equation in t (z)t^3 + (y)t^2 + (x)t + z is satisfied by distinct numbers a,b,c for some x,y,z not all zero So a, b , c must be the three roots of this cubic as they are different Now by viete's relation product of roots = - (constant term)/(coeff. Of t^3) Which gives abc=-1 *** (The last conclusion can be said by saying the given cubic is same as z(t-a)(t-b)(t-c) as they have same roots and t^3 coefficient)
@pravargupta6285
3 жыл бұрын
well you can also use factor theorem of determinants to do easily: As at a=b, |A|=0 so (a-b) is a factor Similarly At b=c, |A|=0 so (b-c) is also a factor At c=a, |A|=0 so (c-a) is also a factor. Now by multiplying diagonals we see that the degree of resultant polynomial will be (1+2+3)=4 and it is homogenous too. So there must be another linear factor in (a,b,c). Let that factor be k(1+abc). Now substitute different values of a,b and c in |A| and find that the value of k is 1. Hence we get the result by multiplying all factors : (a-b)(b-c)(c-a)(1+abc) I am sorry I couldnot give a good explanation why and how to use this amazing method because I did not get it too! I searched up the internet but still didnot find anything. any help would be highly appreciated.!!
@drsonaligupta75
3 жыл бұрын
@@pravargupta6285 did you mean use factor theorem on individual determinants
@pravargupta6285
3 жыл бұрын
@@drsonaligupta75 The theorem actually states that if for some valuw of variable the value of determinant becomes 0 then (x-a) is a factor of the resultant polynomial
@drsonaligupta75
3 жыл бұрын
@@pravargupta6285 understood
@gaurav.raj.mishra
4 жыл бұрын
I always learn something new from every video you make.
@44hwxyz90
4 жыл бұрын
You could just set a=c, the condition doesn't cover that lol
@ЕгорКолов-ч5с
4 жыл бұрын
🤔🤔🤔🤔🤔🤔🤔🤔🤔🤔🤔🤔🤔🤔🤔🤔🤔🤔🤔🤔
@kormosmate2
4 жыл бұрын
Nope. It says a!=b!=c so a!=c also holds.
@mokopa
4 жыл бұрын
@@kormosmate2 1!=2!=1
@user-en5vj6vr2u
4 жыл бұрын
Máté Kormos the != is not transitive
@DavesMathVideos
4 жыл бұрын
A nice but useful little question!
@ramanunnikrishnan7354
4 жыл бұрын
for any Indian in school, this is directly from NCERT and could come in your boards.
@pragati9821
4 жыл бұрын
That's why I found it easy 😂😂
@dasamlan9874
4 жыл бұрын
That's why i did it.
@mohammedafridibeedi3730
Жыл бұрын
Ya it's too easy
@AdoNir
4 жыл бұрын
Writing a≠b≠c is incorrect, because it doesn’t mean a≠c, such that 7≠9≠7 is perfectly true. You should write a≠b, a≠c, and b≠c. (I lost 2 points in a my midterm in linear algebra because I wrote a≠b≠c instead of all the inequalities)
@ffggddss
4 жыл бұрын
It also works to write a≠b≠c≠a If there are 4 or more variables involved, then it's best just to say, "no two of which are equal," or, "all different." Fred
@hybmnzz2658
4 жыл бұрын
That is weird
4 жыл бұрын
I thought the same! a≠b≠c don't implies that a≠c
@prithujsarkar2010
4 жыл бұрын
Woah , mind blown
@davidepierrat9072
4 жыл бұрын
"inequality" isn't the right term, something like 1
@ProfOmarMath
4 жыл бұрын
Vandermonde 😍
@aaravgavshinde
4 жыл бұрын
This is the same example my teacher taught!
@onthecover5042
4 жыл бұрын
Fun fact= If you add one to another one, you’ll get two
@blackpenredpen
4 жыл бұрын
whoa!
@NovayaK
4 жыл бұрын
Mind = blown
@DhruvPatel-qe2yw
4 жыл бұрын
What is the example of det(A+B)=/det(A) +det(B)🤔🤔🤔🤔
@RyanLucroy
4 жыл бұрын
@@DhruvPatel-qe2yw Take A=B=diag(1,1,1). Then det(A+B)=8, but det(A)+det(B)=2
@DhruvPatel-qe2yw
4 жыл бұрын
@@RyanLucroy ohh yeah thanks
@helo3827
4 жыл бұрын
you are the best! Yesterday I was just thinking when can you do a video on matrices, keep it up your videos
@warrengibson7898
4 жыл бұрын
You can check your result by seeing that interchanging any two of (a,b,c) you just change the sign of the det and that’s the same as interchanging two rows of the matrix.
@pravargupta6285
3 жыл бұрын
Well you can also use factor theorem of determinants to do easily: As at a=b, |A|=0 so (a-b) is a factor Similarly At b=c, |A|=0 so (b-c) is also a factor At c=a, |A|=0 so (c-a) is also a factor. Now by multiplying diagonals we see that the degree of resultant polynomial will be (1+2+3)=4 and it is homogenous too. So there must be another linear factor in (a,b,c). Let that factor be k(1+abc). Now substitute different values of a,b and c in |A| and find that the value of k is 1. Hence we get the result by multiplying all factors : (a-b)(b-c)(c-a)(1+abc) I am sorry I couldnot give a good explanation why and how to use this amazing method because I did not get it too! I searched up the internet but still didnot find anything. any help would be highly appreciated.!!
@dbgk2342
4 жыл бұрын
ur beard looks cool
@Liesse_SportSante
3 жыл бұрын
Very good video ! Thanks
@Sam_on_YouTube
4 жыл бұрын
I got a 5 on BC Calculus and placed out of Calc 1 and Calc 2. My very first class in college, the professor with a hard to understand slavic accent writes a matrix on the board and does things with it I had never even considered. I though... oh no. This is going to be tough. I had a much easier time with Calc 4. I understood at least what I was supposed to be doing. My calc 3 (linear algebra) teacher was not very good and I just didn't get it. Then, when I got up to quantum mechanics the following Spring, suddenly I needed to know and use linear algebra and I remembered nothing. Where were you 20 years ago when I was in college?!
@mathophile1912
3 жыл бұрын
O my god I searched for the solution of such question asked in my book. I got this legendary solution
@alexandre6881
4 жыл бұрын
Awesome video!
@zerovibritannia6216
4 жыл бұрын
I am learning Determinant at the moment and this video came up 😀😀
@TheBodyOnPC
4 жыл бұрын
From where do we have that c minus a cannot be equal to 0?
@ZyloSol99
4 жыл бұрын
Goat.
@johannesh7610
4 жыл бұрын
There are easy complex solutions. Let z ≠ 0 be an arbitrary complex number. Set a, b, c to the three complex third roots of z, or one less than those. All of these choices equate the determinant to zero, because of the last column. We can add 3 times the first two columns to it to get (1+a)^3.
@fracaralho
4 жыл бұрын
Why is the determinant of the original matrix equal to the sum of the determinants of the two matrices into which it was broken down?
@eliseuantonio6652
3 жыл бұрын
That's a theorem, I don't remember its name, but you can try proving it yourself by using Jacobi Theorem
@sarthakjain1824
4 жыл бұрын
Did same question before with a wayy longer method
@Dreamprism
4 жыл бұрын
Looks good.
@TheBodyOnPC
4 жыл бұрын
Entire books have been written just about rules of determinants.
@logicalproofs7276
4 жыл бұрын
Logical proofs and Blackpenredpen Both are awesome. 😎😎😎
@RyanLucroy
4 жыл бұрын
When you factored out the abc, you just used the rule det(A*B)=det(A)*det(B) with A=diag(a,b,c), right? Was a bit confused and it took me way longer to figure it out than I would admit 😅
@lordmomstealer
4 жыл бұрын
Sir jiii u are great ♥️❤️ from india🇮🇳
@MyDreamsLullabies
4 жыл бұрын
thank u sir very informative😍😍
@xanthoconite4904
10 ай бұрын
Hi I'm wondering where can I buy the shirt you're wearing in this video, I can only find the cat version on your website.
@Zeusbeer
4 жыл бұрын
Why not just devide the (abc+1)*matrixdet = 0 by matrixdet on both sides to get abc+1 = 0 -> abc = -1 ?
@alejrandom6592
3 жыл бұрын
by a/=b/=c can we infere that a might be equal to c?
@priyanshsingh1753
4 жыл бұрын
In that much space and time I'd solve it directly.
@خوارزميخوارزمي-ص1ص
4 жыл бұрын
why not 3, 1/3,-1 and many values multiple it -1
@MEBVishwaS
4 жыл бұрын
I approached differently which gives me different answer. I maybe wrong. By manipulating the row i just got( a^3+ka^2+Ka+1) I solved it to get three different roots which a,b,c. So then the matrix becomes zero. -1 is one of the root. So divided it by X+1 to get quadratic equation. By the quadratic formula I changed k to get different values of b and c which should solve it. I don't know where I'm wrong.
@integralof2880
4 жыл бұрын
Nice example. ☺
@kusoae
4 жыл бұрын
His beard is looking so weird 😂😂
@ameersahi2168
4 жыл бұрын
Why when you chnage coluom 3 by coluom 1 mulitply by -1?
@jayantverma2136
4 жыл бұрын
Well i solved it a few days ago..its an standard indian ncert problem
@alainrogez8485
4 жыл бұрын
Can we prove the sum of determinants BpRp did in the beginning? Is it legitimate?
@Med_Alzubaidi
4 жыл бұрын
❤
@shivansh668
4 жыл бұрын
Make a vdo on the ques of abstract ALGEBRA
@cristianv2850
4 жыл бұрын
The way I saw a≠b≠c is like this: We start out by using statements of logic. a -> ~b b -> ~c Taking the inverse of the second statement, we get ~b -> c. We can conclude that a -> c, thus A = C.
@sushantyadav7806
4 жыл бұрын
Some different method please
@addicted7766
4 жыл бұрын
tremendous
@manamtiwari
4 жыл бұрын
Can you make more on matrices and determinants please. 🤗🤗🤗🤗🤗🤗🤗🤗🤗🤗🤗🤗🤗🤗🤗🤗🤗
@Visputescooking
4 жыл бұрын
You please actually start to teach precalculus till the calculus... Me and many people like me can just read the calculus in this age. Please let us see the calculus 🙏 please sir 🙏
@blackpenredpen
4 жыл бұрын
?
@Visputescooking
4 жыл бұрын
@@blackpenredpenPlease sir🙏 you can just open a brand new channel in which you teach(something).
@joacinhof3style37
4 жыл бұрын
1:35 c^3 twice lol, he wrote ^3 cuz he said "third column" at the same time
@ffggddss
4 жыл бұрын
(I'm assuming you meant, a ≠ b ≠ c ≠ a.) After a bunch of reductions and factoring, I wind up with that determinant = (b - a)(c - a)(c - b)(1 + abc) Setting that = 0, with the inequality condition rules out any of the first 3 factors being 0; that leaves only abc = -1 So any three unequal values whose product is -1, solves it. @bprp: How ya doin? I heard a rumor you were hospitalized for a while. PS: Love the shirt! Fred
@blackpenredpen
4 жыл бұрын
Hi Fred, I was! I had surgery about a month ago to remove my appendix. Luckily it was just a one-day thing and I was fine after that (except for some usual pain from the wounds). Thank you. How are you? I hope you are doing well, too.
@ffggddss
4 жыл бұрын
@@blackpenredpen That was what I thought it probably was, from what I heard. Glad you came through it all right. One benefit of that, which most of the rest of us don't have, is you no longer have to worry about your appendix!! No complaints here, either. I and my housemate got tested for COVID today because someone at the shop her boyfriend works in, tested positive. Two results to come; one tomorrow, and a more definitive one in 5 days. I expect negatives. Meanwhile, I posted my first YT video! It's in the MegaFavNumbers playlist that James Grime (singingbanana) established. I'm not entirely satisfied with it; I need better equipment, and I was somewhat rushed because I was getting in so close to the deadline (Sep 2). I haven't watched all those yet; I think I saw you had one, which I will watch soon. Fred
@mahfuzhasan576
4 жыл бұрын
Woah you grew your beard out. Nice.
@tomatrix7525
4 жыл бұрын
Epico
@呂永志
4 жыл бұрын
我記得 a不等於b不等於c 這種寫法,a可能等於c。
@langhuningtha8774
4 жыл бұрын
A challenge for blapenredpen : √4x^3-√x=√x+192
@kushagrakapoor2105
4 жыл бұрын
Am I the only one who feels that bprp is the quang tran of maths?
@jumpierwolf
4 жыл бұрын
Your old beard looks nicer.
@hamiltonianpathondodecahed5236
4 жыл бұрын
imma just gonna pretend dat I knew all that EDIT: And the description is killing me (≧▽≦)
@logicalproofs7276
4 жыл бұрын
Is this possible that 1+1/n=1/n. 🤔
@kusoae
4 жыл бұрын
No
@MEBVishwaS
4 жыл бұрын
If n=0
@kusoae
4 жыл бұрын
@@MEBVishwaS n can never be zero since it would make 1/n undefined
Пікірлер: 107