Matrices were so weird when I started studying Linear Algebra about 6 years ago. Completely different from everything that I had seen up until then. "What, I am supposed to do math on these weird number tables?"
Hi BlackPenRedPen. Your mathematics teaching is very unique on TH-cam. I like how you use the old school method of using a white board as it is very engaging. Do you have any tips on how to grow a developing maths channel like mine on TH-cam. Thanks man, I hope you reply to this question.
Thanks and hi there. You may check out my video here, where I summarized what I have learned along my YT journey. th-cam.com/video/A6oxpzea92k/w-d-xo.html
I love this new series of videos. Its always good to have new (not so new) content. I mean, I love the integrals videos but for a long time follower sometimes it gets repetitive. Anyways, thanks for the content. Peace
"If A and B are symmetric, does AB also have to be symmetric?" No, because t(AB)=t(B)×t(A)=BA, and the multiplication on the ring of square matrices is NOT commutative.
"If A and B are symmetric, does AB also has to be symmetric" No, because of 2 reason. First, for AB to be symmetric, it has to exist. Thus A and B must have the same dimension. There is no condition saying explicitly saying, therefore AB might not exist. Second, t(AB) = t(B)*t(A) = BA =/= AB.
Lets try a general 2x2 times a 2x2. [a b , b c] times [d e , e f]. the result we get is [ad+be ae+bf , bd+ce be+cf], since none of these variables have to be equal to each other, AB will only be symmetric for a 2x2 matrix if ae+bf = bd+ce.
Hello BlackPenRedPen, I wanted to ask a question from you, ..that how can we solve for the real solutions of an irrational degree equation? For example, x^(√2) -3x +2 = 0 (it has two real roots) One of its solution is 1. But What algorithm we must use here to find the other real root Please reply
Well, you present a nice puzzle. . . 1. because the square root of two is not a rational number, we can't subitute a certain y=x^a such that your equation turns into a polynomial equation in y. 2. but on the other hand, by already presenting that it has two real roots as well as that one of these is 1, we can make a start by saying: (x^a-1)(b*(x^c)-d)=0=x^(2^1/2)-3x+2 If we can find an a,b,c and d combination that fits this equation, then our roots are *1^1/a* (which we already knew) and *(d/b)^(1/c)* . To find this _(a,b,c,d)_ combination we can maybe employ linear algebra.
if A and B are symmetric, is AB symmetric? A=A^T, B=B^T (def of symmetric) check M^T=M: (AB)^T= B^T A^T = BA matrix multiplication is not commutative so (AB)^T=BA is not always equal to AB and so AB does not have to be symmetric
@@Joffrerap [a1 a2] [b1 b2] = [ - a1b2+a2b3] [a2 a3] [b2 b3] [ - - ] Thats AB and you can see that BA would be similar, but with b1a2+b2a3 (switch a and b) in that entry, which is different, so AB != BA
If f(x) = 8-log(x). Can you please do find the inverse (that is the easy part), but can you show how to find the intersection point? Can you please show how to tell if the intersection point occurs on the x or y-axis or just in a quadrant? That was a bonus question in our Calculus 2 class? He wanted to test our Algebra knowledge. No one got it correct. Our class was last semester online so I never knew how to find the result. By the way, I love your beard. The professor does not want decimals. He wanted exact answers. He said that would stop people from using Desmos. Thank You so much, Sir. It would be greatly appreciated if you can make a video on that.
Hey BlackPenRedPen, I have a question for you I am unable to solve it Find the principal values of x in tan(X)=2^(sin(X)+cos(X)) Hope you will help me with it 👍
Hi Blackpenredpen, I have a question: find the value of ln(x+ln(x+...)) where x>=1. I found this sequence but I have trouble solving it. Hope you help me.
I have a question: ((99/5 + (12 I)/5)^(-(28/5) + (79 I)/5))^(61/10 + ( 143 I)/10)= (99/5 + (12 I)/5)^(-(2601/10) + (163 I)/10) Mathematica, and Wolfram Alpha say no, but I don’t know why?
what do you get when you have a number raised to the power of a matrix? Do you just distribute the calculation to each element equally, or is it some other form....i can't seem to find anything online about it. I am trying to come up with a cryptographic routine using matrix keys.
That differential equation is actually linear. It would be nonlinear if it had sin(y) instead of sin(x). The term you might be looking for here is non-homogeneous, and it is fairly straightforward to tackle with the method of undetermined coefficients.
How about [1 0, 0 1] and [1 0 0, 0 1 0, 0 0 1] ? Both are forms of I and hence symmetric, but due to having different dimensions, their product does not exist and is hence not a symmetric matrix.
@@xwtek3505 I know that that "have to" is the key: it implies that when you show an exception to the claim you disprove it, which is what both almightyhydra and I did. *BPRP* tells it in the video himself.
I don’t know anything about linear algebra. I’ll leave a comment on the last video in this category explaining my knowledge as of that video. Edit: I’m watching these backwards… hold on.
Ive beed good proffesor. School has definitely been overwhelming. Its harder now. Ive been learning how to get through this. Ive take up running, running helps clear my mind and helps me focus. Ive been doing 30 min runs 3 times per week. I know life will get better soon, im trying keep myself motivated and positive. How about yourself?
Ed Rodriguez I have been good, too. Thanks. I got a squat stand and a weight bar recently so I will starting lifting weights. Btw, I am requiring my calc 2 students to do video projects this semester. They are finding fun in them. So that’s good. Best luck for you in your studies and everything!
![เปิดใจ พี่ญา คนรุม หลังทัวร์ลง หนักสุดในชีวิต!! l [Nickynachat]](http://i.ytimg.com/vi/2-OJZRtclro/mqdefault.jpg)
I need a linear algebra t-shirt soon!
Hello blackpenredpen i am your big fan
But why do you upload so late
Its 3 am in the night
OoO Interesting!
Shreyan Narula clearly youtube takes a long time to upload or you are in different time zones.
Matrices were so weird when I started studying Linear Algebra about 6 years ago.
Completely different from everything that I had seen up until then.
"What, I am supposed to do math on these weird number tables?"
Wait until you use tensors
Woah!..the t-shirt with indeterminate forms...
I love it 🙃
I don’t know about symmetric matrices, I only know about orthogonally diagonalizable ones 😂
Oh well, I am not there yet... go away lol
Actually in english it’s spelled matrices.
Colleen Silly autocorrect haha
Matrices* typo lol
That matrix was almost as nice as your beard!
Hi BlackPenRedPen. Your mathematics teaching is very unique on TH-cam. I like how you use the old school method of using a white board as it is very engaging. Do you have any tips on how to grow a developing maths channel like mine on TH-cam. Thanks man, I hope you reply to this question.
Thanks and hi there. You may check out my video here, where I summarized what I have learned along my YT journey. th-cam.com/video/A6oxpzea92k/w-d-xo.html
@@blackpenredpen Thanks so much for responding to my question! You are the first to do it. I will definitely watch your guide.
I love this new series of videos. Its always good to have new (not so new) content. I mean, I love the integrals videos but for a long time follower sometimes it gets repetitive. Anyways, thanks for the content. Peace
Wow you actually took my advice of wearing a white t 👌
It actually a very light blue tee : )
. I thought it would be somewhat visible on camera.
I hung up the phone on my gf because bprp uploaded
@hawkturkey Math addiction is good
Girlfriend is temporary math is eternal
Only if A and B are also commutative. Kinda obvious.
yes my first BPRP linear algebra vid!
"If A and B are symmetric, does AB also have to be symmetric?"
No, because t(AB)=t(B)×t(A)=BA, and the multiplication on the ring of square matrices is NOT commutative.
BA =/= AB so it's not necessarily true for any A & B.
@@romaindec1717 if AB exists, BA doesn't exists UNLESS both are square and have the same dimensions, anyway.
@@seroujghazarian6343 yes, so many things to precise, this is why maths are boring sometimes
Wanna try this? Prove by induction that n³≤ 2^n, for all integers n with n ≥ 10.
Hello from Turkey!
"If A and B are symmetric, does AB also has to be symmetric"
No, because of 2 reason. First, for AB to be symmetric, it has to exist. Thus A and B must have the same dimension. There is no condition saying explicitly saying, therefore AB might not exist. Second, t(AB) = t(B)*t(A) = BA =/= AB.
Lets try a general 2x2 times a 2x2. [a b , b c] times [d e , e f]. the result we get is [ad+be ae+bf , bd+ce be+cf], since none of these variables have to be equal to each other, AB will only be symmetric for a 2x2 matrix if ae+bf = bd+ce.
BlackPenRedPen: Hello Linear Algebra!!
Me: 👁👄👁
thank you
Hi! I just saw your old video on sin(z)=2. Could you make a new one on how to graph a function like that?
I like your t-shirt.
7 indeterminate forms
Hello BlackPenRedPen,
I wanted to ask a question from you, ..that how can we solve for the real solutions of an irrational degree equation?
For example, x^(√2) -3x +2 = 0
(it has two real roots)
One of its solution is 1. But
What algorithm we must use here to find the other real root
Please reply
Well, you present a nice puzzle. . .
1. because the square root of two is not a rational number, we can't subitute a certain y=x^a such that your equation turns into a polynomial equation in y.
2. but on the other hand, by already presenting that it has two real roots as well as that one of these is 1, we can make a start by saying:
(x^a-1)(b*(x^c)-d)=0=x^(2^1/2)-3x+2
If we can find an a,b,c and d combination that fits this equation, then our roots are *1^1/a* (which we already knew) and *(d/b)^(1/c)* .
To find this _(a,b,c,d)_ combination we can maybe employ linear algebra.
if A and B are symmetric, is AB symmetric?
A=A^T, B=B^T (def of symmetric)
check M^T=M: (AB)^T= B^T A^T = BA
matrix multiplication is not commutative so (AB)^T=BA is not always equal to AB and so AB does not have to be symmetric
that's not really a proof since you didn't show there is an example of two symmetric matrices that doesn't commute
@@Joffrerap
[a1 a2] [b1 b2] = [ - a1b2+a2b3]
[a2 a3] [b2 b3] [ - - ]
Thats AB and you can see that BA would be similar, but with b1a2+b2a3 (switch a and b) in that entry, which is different, so AB != BA
@@user-en5vj6vr2u yes this coefficient would be b1a2+b2a3 so would be different for b1=b2=0 and b3=a2=1
Challenge: give an nxn example for arbitrary but fixed n. This is very easy once you did it for 2x2.
@@Grassmpl no
Hello from Poland🙃🙂
If f(x) = 8-log(x). Can you please do find the inverse (that is the easy part), but can you show how to find the intersection point? Can you please show how to tell if the intersection point occurs on the x or y-axis or just in a quadrant? That was a bonus question in our Calculus 2 class? He wanted to test our Algebra knowledge. No one got it correct. Our class was last semester online so I never knew how to find the result. By the way, I love your beard. The professor does not want decimals. He wanted exact answers. He said that would stop people from using Desmos. Thank You so much, Sir. It would be greatly appreciated if you can make a video on that.
you are my favorite youtuber! Love your linear algebra stuff! Keep it up, BTW, it would be nice if blackpenredpen can respond to this
XD
I've started school today.and it's calculus about matrix.😚
Your school started today? That’s pretty late!
@@blackpenredpen Ohh it not late, it's faster than other school in my country.😁
Hey BlackPenRedPen,
I have a question for you
I am unable to solve it
Find the principal values of x in
tan(X)=2^(sin(X)+cos(X))
Hope you will help me with it 👍
Saludos desde Ecuador.
Buen video.
Can you do a video on a matrix A where the transpose of matrix A is also the inverse of matrix A?
Coming up!
Hi Blackpenredpen, I have a question: find the value of ln(x+ln(x+...)) where x>=1. I found this sequence but I have trouble solving it. Hope you help me.
I have a question:
((99/5 + (12 I)/5)^(-(28/5) + (79 I)/5))^(61/10 + ( 143 I)/10)= (99/5 + (12 I)/5)^(-(2601/10) + (163 I)/10)
Mathematica, and Wolfram Alpha say no, but I don’t know why?
Man. your beard looks dope
Nice
From where u r getting such T-shirts 😄 btw the way u teach is SOOOOOOOOOOOOOOOOOOOOO good 😎😘
Beard looking fire🔥
Mashallah brother has grown beard.👍👍
symmetrix
dunno but that kinda rhymes with symmetric
Dude these vids would have been helpful when I took linear algebra last semester 😞. Jk man love the videos
YOU GOOD
Watched the entire video waiting for him to summon Charizard 😊
كم انت رائع يا رجل (:
what do you get when you have a number raised to the power of a matrix? Do you just distribute the calculation to each element equally, or is it some other form....i can't seem to find anything online about it. I am trying to come up with a cryptographic routine using matrix keys.
I think you need to turn that whole matrix into number than do the calculation. But i have also failed to find a source referencing this.
Why don't you use a lapel mic
liking the beard man
Good afternoon
when will you make a "100 limits" video??
I like sym- *metrix*
Hey blackpen, i'm 16 from indonesia. I have a problem in Ordinary Diferetial Equation non linear 2 order. y''+4y'+(196/3)sin(x)=0. Help me, please☺️
That differential equation is actually linear. It would be nonlinear if it had sin(y) instead of sin(x). The term you might be looking for here is non-homogeneous, and it is fairly straightforward to tackle with the method of undetermined coefficients.
There's also integrating factor if you solve for y' first.
is linear algebra harder than calculus?
I think the thumbnail had a stroke
好久不見！
I would love to watch your videos but I just can't understand a thing
Let's try [1 2, 2 1] x [2 3, 3 4]
= [8 11, 7 10] which is not symmetric. ✓
How about [1 0, 0 1] and [1 0 0, 0 1 0, 0 0 1] ?
Both are forms of I and hence symmetric, but due to having different dimensions, their product does not exist and is hence not a symmetric matrix.
@@Apollorion the key word is have to. It means that the answer is true only if AB is symmetric for A and B symmetric.
@@xwtek3505 I know that that "have to" is the key: it implies that when you show an exception to the claim you disprove it, which is what both almightyhydra and I did. *BPRP* tells it in the video himself.
@@Apollorion Oh, I see. I thought since you're bringing up identity matrix, I thought you were finding the case where it is still symmetric.
مرحبا🍁😊
I don’t know anything about linear algebra. I’ll leave a comment on the last video in this category explaining my knowledge as of that video.
Edit: I’m watching these backwards… hold on.
I lost hope in humanity
Blue pen? blue pen!!!
i cant trust anything any more
hello!
Hello
Why are carrying the microphone by your hand while you can use both the hands for hand gestures and better explanation?
I miss school
Same here. How have u been Eddie?
Ive beed good proffesor. School has definitely been overwhelming. Its harder now. Ive been learning how to get through this. Ive take up running, running helps clear my mind and helps me focus. Ive been doing 30 min runs 3 times per week. I know life will get better soon, im trying keep myself motivated and positive.
How about yourself?
Ed Rodriguez
I have been good, too. Thanks. I got a squat stand and a weight bar recently so I will starting lifting weights. Btw, I am requiring my calc 2 students to do video projects this semester. They are finding fun in them. So that’s good.
Best luck for you in your studies and everything!
lindo
I miss olimpiad problems
First like, then watch :)
I liked then entered comments
Why do you upload so late 😆
I bet no one will respond to this
you lost
簽到
nice beard hahaha
crack
first
nice
Plz be more extreme. Beard with bald, lol