Hey buddy, I want to thank you for taking on a matrix without 0's because most of these youtube videos i've come across have 0's at the top or bottom and its annoying because the problem i'm tryin to solve is anything but 0's! Thanks!
Your videos on linear algebra have so far been very helpful. I'd love videos on Diagonalisation of matrices, coordinate transformations and Jordan block decompositions. Thanks!
FOR THOSE STUCK ON 11:05: Apply synthetic division to the lambda equation that is given. Divide the polynomial by (x-1). After doing that, you should get the values (zeros) 1, 2, 21. The reason 1 is included is because the synthetic division ending in 0 allows that factor to be included in your solution as an eigonvalue.
@@DevStuf by rational root theorem, you basically find out rational roots of a number that doesn't contain lambda, or a constant, in this case is -42, so the roots of -42 is plusminus1,2,3,6,7,14,21,42 , usually you'd test root 1, if your function equals to zero, that's the number you divide by, such as 1
there's a shortcut to the eigen values he solved for and it works; λ^3 - (sum of diagonal of the matrix)λ^2 + (sum of the diagonal of the adjoint of the matrix)λ - (the determinant of the matrix)
Outstanding explanation, thank you for sharing. I also like how you pronounce the number 3, you make it sound like in my lenguage, Spanish (pachuco mode)
@@SkanCityAcademy_SirJohn it's my pleasure to get a teacher like u ... I'm pursuing masters degree in economics but maths teacher isn't so good that's I was finding a teacher who can explain these things straight forward.... ❤️❤️Thank u so much again sir
It is in Row echelon form. For Row echelon form, diagonal entries are 1 and the elements of the upper triangular matrix can be any other value. Unless in a case where the elements in a row are all zeros, then it is adviced to put that row at the button. While for reduced row echelon looks like the identity matrix
This is awesome! I was wondering, is the best way for this usually the cofactor expansion? Or if we happen to have 1's in our matrix do you think it is more worth it to do Chio's decomposition to make it one dimension lower? I tried the normal 3x3 trick where we add the first two columns on the outside of it to do that but i found this pretty messy
@@SkanCityAcademy_SirJohn honestly I don’t know I guess it depends. This cofactor expansion would be nicest in the case everything else were zeros up top. And you have to get lucky for chio bc the whole diagonal is already excluded due to the -lambda part. I learned Chios condensation a bit ago and I think it’s so cool, it’s just that I rarely find a chance to use it 😂
@@SkanCityAcademy_SirJohn I’m from America, and I’m just taking some intro to linear algebra class. I like learning math on my own sometimes too so I just happened across Chios condensation one day. I wish we’d learn more cool tricks like that too. Just right now I learned that the characteristic equation for 3x3 is λ^3 -trace(A)*λ^2+Diagonal Minors(A)*λ - |A| = 0. If you have any cool tricks too (determinants, eigenvalues or vectors, etc), please recommend them even if they might be a bit above my current level 😅
not necessarily, the aim is to convert the given matrix to an upper triangular matrix with the leading diagonals being 1. however when there is a zero row, ie a row with all zeros, it should be at the buttom.
Got lost after 10:32 what should i be searching for to know how to get the values, Are supposed to test all numbers from 1 to n until we get 3 values that make it 0?
i think i get you, at that point you can use your calculator to get the three values, or you can investigate from 1 to n, with constant practice you will know the numbers that are likely to fit the equation. Meanwhile you can watch this video ua-cam.com/video/4kOrkFOfCtI/v-deo.html
@@SkanCityAcademy_SirJohn I feel if i am in an exam room and have to test all numbers from 1 to n, I'm stuck on 1 question the whole time if the number is like 25 for example, Thanks for the link to polynomials though, this looks promising
at 10:49 can you make it clear how did you get lamda 1,2 and 3 also i don"t know how to do it on the calculator if you can reply fast cuz i have an final exam the day after tomorrow
It's a cubic function and hence you need to obtain 3 roots. To do it on the calculator Mode 5 4 Type the coefficients of the function a, b, c,d, for any one punch equal to for next, you will get the roots
@@SkanCityAcademy_SirJohn Alright thanks a lot sir for your reply, your video is really helpful. I thought there must be some mathematical reason. Thanks for clearing this. I also prefer charahteristic polynomial, it somehow just clicks in my brain although it is slow process. One quick question, is it necessary to calculate REF as well for computing an eigen vector ? what if we just a put a quadratic equation directly without computing REF ?
Bro can I send you one example on custom vectors. I've been counting for maybe 3 hours and I can't get to the vector. I'll send you some money for coffee if you want :D
I have two original equations with three unknowns ( X, Y, Z). I've just added one extra equation to make the original equations solvable. What should I call this adding process in mathematics? I just need the correct wording for that. Any help would be appreciated. Thanks
You can combine the factor theorem and the long-division method to obtain the factors of the polynomial. hope you are familiar with the two mentioned above. Especially with the factor theorem, if f(x) is a polynomial of degree more than one and 'a ' is a number, then if f(a) is zero, then (x-a) is a factor of f(x).
You just need to use the factor theorem. You put x = a into the cubic function, if it's zero, the x-a is a factor of the cubic function. Which means you already have one eigen value. The you divide the cubic function by the new factor x-a to obtain a quadratic function, then you find it's factors and the corresponding x values
this is because, according to the rule for reduced row echelon form, whenever there is a zero row (a row with all zeros), it must be placed at the last row, hence we interchanged the rows.
![Diagonalizing 3x3 Matrix - Full Process [Passing Linear Algebra]](http://i.ytimg.com/vi/0kA_VqHSpGg/mqdefault.jpg)
This is so straightforward. What a good teacher! Many thanks.
Awww thanks so much
So amazing teacher explained clearly. Can I request a lecture on complex root and equal root
Thanks for existing man
Thanks be to God
16:03
The reason is that since the RHS is zero, dividing through by 10 to obtain 1 does not change the value of x3, so it can be ignored.
Understandable 😊
@peridakingani thanks so much
Hey buddy, I want to thank you for taking on a matrix without 0's because most of these youtube videos i've come across have 0's at the top or bottom and its annoying because the problem i'm tryin to solve is anything but 0's! Thanks!
You are most welcome, keep watching for more great content. I really appreciate your comments.
Where do you watch me from?
Thanks very much for this teaching
Much love ❤ and respect from zambia 🇿🇲🇿🇲🇿🇲
Thanks so much, Kasanda, I appreciate it.
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Thanks for this. You are explaining directly from your heart, with care and love
Thanks so much for watching, best wishes
Your videos on linear algebra have so far been very helpful. I'd love videos on Diagonalisation of matrices, coordinate transformations and Jordan block decompositions. Thanks!
Thanks so much.
Kindly check this playlist
ua-cam.com/play/PLInywrvFyvq7oAlPscVnXsd8CRTsh0b77.html
Very clear explanations. This was very helpful. Thank you
You are welcome
Number one idea to my coursework,big up tutor
Great... Thanks so much
now making sense indeed thank you a lot
You are most welcome
FOR THOSE STUCK ON 11:05:
Apply synthetic division to the lambda equation that is given. Divide the polynomial by (x-1). After doing that, you should get the values (zeros) 1, 2, 21. The reason 1 is included is because the synthetic division ending in 0 allows that factor to be included in your solution as an eigonvalue.
how do you know what to divide by?
@DevourOrGetDevoured please kindly state the time in the video so I help you out.
@@SkanCityAcademy_SirJohn found out why alr
YEP
@@DevStuf by rational root theorem, you basically find out rational roots of a number that doesn't contain lambda, or a constant, in this case is -42, so the roots of -42 is plusminus1,2,3,6,7,14,21,42 , usually you'd test root 1, if your function equals to zero, that's the number you divide by, such as 1
This is the best channel ever
God bless you ❤
Amen. And good luck
What a good teacher so precise
Thanks so so much
Absolute cinema! i have final exam on Tuesday and you just saved me
Aww I guess that's a great feeling for you.
It's interesting how we're doing same mathematics all over the world 😂😂
I'm watching from Kenya and I'm really grateful for the video
Aww thanks so much
Excellent tutorials. Thank you.
You are most welcome, and good luck
this lesson is very awesome , thanks so much ☺
You are most welcome
I've got a test today and this is all. I needed
That's great. Best wishes
Kardeşim çok teşekkür ederim. Harika bir ders. Çok basit olarak anlatmışsın. Tebrik ederim.
thanks so so much
there's a shortcut to the eigen values he solved for and it works;
λ^3 - (sum of diagonal of the matrix)λ^2 + (sum of the diagonal of the adjoint of the matrix)λ - (the determinant of the matrix)
Thanks so much for input❤️❤️
Thank you from Sri lanka! 🙏
Youre most welcome
amazing teaching method
thanks so much for your comment. And good luck in your academics
At @10:45 How can the eigen value be 1. If lambda=1. Then 1-24+63-42=-2 which is not equals to zero.?Once please verify.
It 65, no 63, so it will be 1-24+65-42 which equals 0
@@Warchler got it. Thanks..!
It’s to much helpful, love you man ❤❤
Thank you so so much
Best teacher ever you are GOAT.
Aww... Thanks so much. Keep watching for more
Outstanding explanation, thank you for sharing. I also like how you pronounce the number 3, you make it sound like in my lenguage, Spanish (pachuco mode)
Hahahah thanks so much, and nice meeting you.
Thanks man. Well explained....the video is long but it's worth it :)
Thanks so much
Thank you my friend, you made it a lot more digestible. What a teacher!!
You are most welcome. Please keep watching for more
Godddd bless youuu I've been struggling the wholeee day to understand thisss❤❤❤❤❤❤
That's great, thanks you got sorted at the end. Where do you watch from?
@@SkanCityAcademy_SirJohn UAE 🇦🇪
@idontcare7667 that's fine, im from Ghana 🇬🇭.
@idontcare7667 Muslim or Christian?
From your accent, I could spot you're my Ghanaian brother..... Watching your video from the States.
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That is correct. I'm a Ghanaian
That's great, are you doing postgrad studies?
thank you for the video, you helped med a lot.
You are most welcome
Masterpiece. Writing my exam this morning. It sure would save me 😊
Yes please, good luck
@@SkanCityAcademy_SirJohn thanks, I love you
@wangster331 aww thanks so much
Where do you watch from
From Nigeria
@wangster331 great
Thanks, this is very simple explanation
You are most welcome
God richly bless you🙏🏽
Amen... thank you very much. best wishes
This is so easy after listening to this. Tysm! 😭
Thanks so much for your comments and good luck in your studies.
your videos are really helpful for calculus and linear algebra, thank you!!
You're most welcome. And thanks for your kind words too.
Spectacular Explanation.
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Most welcome
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thanks so so much....I'm grateful
For the first eigenvalue, I thought it should not have zero as a value@@SkanCityAcademy_SirJohn
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thanks so much Steven
Explanation is very good and clear. Keep it up.
Thank you so much
@@SkanCityAcademy_SirJohn one of these questions came during my exams and I was able to attend it thankyou
Aww you are most welcome.
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You're welcome
Thanks for watching
You saved me from failing my exam for the 4th time
Wow, that's great
Dang 4 times that’s crazy. Fr though this dude has the best explanation
How did you get out? Lamda? Final output ? @@SkanCityAcademy_SirJohn
Well understood... Thanks
Most welcome
Thanks so much ❤❤❤
You are most welcome
Thank you from India♥
You are welcome
Please how you found lambda with third equation like in the video (10:32)
It's a cubic equation, just punch on your calculator
Think you sif❤❤
Nice and reasonable solution
Thanks so much
17:33 why do you pick an arbitrary value for x2 but not x1? Will or does it make any difference?
Oh no, it doesn't make any difference, you can either choose for x1 then you use that to find x2. It depends on your preference.
But if there is a negative it will definitely affect your answer, won’t it?
@viktordowa please a negative where
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Thanks so so much
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thanks so so much. good luck today
Love from Kashmir 🍁❤️
Thanks so so much
@@SkanCityAcademy_SirJohn it's my pleasure to get a teacher like u ... I'm pursuing masters degree in economics but maths teacher isn't so good that's I was finding a teacher who can explain these things straight forward....
❤️❤️Thank u so much again sir
@rizwann098 you are most welcome
Wow .....I love this explanation
Thanks so so much
Appreciate your lecture sir
Amen and thanks
How we find these eigen values that you write??
16:53 For lamda 1 ,i think the matrix was not in its row echelon form,if it was can u explain further??
It is in Row echelon form. For Row echelon form, diagonal entries are 1 and the elements of the upper triangular matrix can be any other value. Unless in a case where the elements in a row are all zeros, then it is adviced to put that row at the button. While for reduced row echelon looks like the identity matrix
This is awesome! I was wondering, is the best way for this usually the cofactor expansion? Or if we happen to have 1's in our matrix do you think it is more worth it to do Chio's decomposition to make it one dimension lower? I tried the normal 3x3 trick where we add the first two columns on the outside of it to do that but i found this pretty messy
Wow, really
@@SkanCityAcademy_SirJohn honestly I don’t know I guess it depends. This cofactor expansion would be nicest in the case everything else were zeros up top. And you have to get lucky for chio bc the whole diagonal is already excluded due to the -lambda part. I learned Chios condensation a bit ago and I think it’s so cool, it’s just that I rarely find a chance to use it 😂
yes actually@@darcash1738
where do you watch me from? which program do you read and level?@@darcash1738
@@SkanCityAcademy_SirJohn I’m from America, and I’m just taking some intro to linear algebra class. I like learning math on my own sometimes too so I just happened across Chios condensation one day.
I wish we’d learn more cool tricks like that too. Just right now I learned that the characteristic equation for 3x3 is λ^3 -trace(A)*λ^2+Diagonal Minors(A)*λ - |A| = 0. If you have any cool tricks too (determinants, eigenvalues or vectors, etc), please recommend them even if they might be a bit above my current level 😅
its so tebeda thanku
You are most welcom
THANKS A LOT
You're welcome!
thank you!!!
You are most welcome
How can we find the eigen values by calculater??
Thank you very much
You are most welcome
When solving for lambda 3, column 3 row 3 isn’t it supposed to be -20? 28:40
No please, it's -10-(-10) = -10+10=0
Does the order in which you choose the value for lambda matter?
No please, the order doesn't matter
Thank you!🙂
You're welcome, where do you watch from?
@@SkanCityAcademy_SirJohn I am from Kenya.
That's great, thanks for watching
Excellent
thanks so much
hey , so for the values of eigenvector , our aim should be making R3 to 0 ?
not necessarily, the aim is to convert the given matrix to an upper triangular matrix with the leading diagonals being 1. however when there is a zero row, ie a row with all zeros, it should be at the buttom.
god bless you thank you so much
thanks so much
very good explanation
Thanks so much Edvin
Thank much for this video it really help
You're nost welcome
Got lost after 10:32 what should i be searching for to know how to get the values,
Are supposed to test all numbers from 1 to n until we get 3 values that make it 0?
i think i get you, at that point you can use your calculator to get the three values, or you can investigate from 1 to n, with constant practice you will know the numbers that are likely to fit the equation. Meanwhile you can watch this video ua-cam.com/video/4kOrkFOfCtI/v-deo.html
@@SkanCityAcademy_SirJohn I feel if i am in an exam room and have to test all numbers from 1 to n, I'm stuck on 1 question the whole time if the number is like 25 for example,
Thanks for the link to polynomials though, this looks promising
Youre welcome
You'll test factors of 42 only...Both positive and negative numbers
Great 👌👍
Thank you so much
Bless you, but so you have any videos about vector spaces and spaning a vector.
Amen. No please
Do you always have to make the last line to have all zeros or if you want you can just calculate without making the last line all zeros
Not necessarily, but if there appears a zero row, then it should be at the button
Great explanation 👍
thanks so much for watching
at 10:49 can you make it clear how did you get lamda 1,2 and 3 also i don"t know how to do it on the calculator if you can reply fast cuz i have an final exam the day after tomorrow
It's a cubic function and hence you need to obtain 3 roots. To do it on the calculator
Mode
5
4
Type the coefficients of the function a, b, c,d, for any one punch equal to for next, you will get the roots
@@SkanCityAcademy_SirJohn thanks man i appreciate it you are the best
Thanks so much, El Molla
Please for the cubic equation if u get the values to be decimals, How do we solve it
Usually you will get whole number values, if you get decimals, kindly check if the cubic equation is right
@@SkanCityAcademy_SirJohn okay thanks
Any reason why you are not using krammer's rule which is much simpler than using charachteristic polynomial equation ?
No reason please, you can use crammer's to solve as well.
@@SkanCityAcademy_SirJohn Alright thanks a lot sir for your reply, your video is really helpful. I thought there must be some mathematical reason. Thanks for clearing this. I also prefer charahteristic polynomial, it somehow just clicks in my brain although it is slow process. One quick question, is it necessary to calculate REF as well for computing an eigen vector ? what if we just a put a quadratic equation directly without computing REF ?
Thank you very much Sri
You are most welcome
How did you jump to 21 as the value lambda
Those are the roots of the equation
Amazing
Excellent explenation. But one point. How i get lamba 1,2,21 without calc ?
On your calculator, press mode, then equation in the form ax³ + bx²+cx = 0
Then type in the values of a b c and d as in the equations
@@SkanCityAcademy_SirJohn And if i cant use calc i must use cubic equation or is there another variety ?
@@norgac9103 you can use the factor theorem
Thank you .
Bro can I send you one example on custom vectors. I've been counting for maybe 3 hours and I can't get to the vector. I'll send you some money for coffee if you want :D
In finding eigen values of 21, why did we use row two as the pivot row for reduction and not row 1
answer this question
great jobbbbbb. thanks
You are welcome
𝐓𝐡𝐚𝐧𝐤 you
You are most welcome
well simplified. Gracias
Thanks so so much
I have two original equations with three unknowns ( X, Y, Z). I've just added one extra equation to make the original equations solvable. What should I call this adding process in mathematics? I just need the correct wording for that. Any help would be appreciated. Thanks
how did you get the roots of the equation, I mean how did you get the eigen values.
I used a calculator.
🎉 thankyou
You are most welcome
Pls what are we to make 0
Howmany of the values
Can you please come again? I don't get your question
when calculating the eigenvectors in the case lamda equals to 1, can i just let the x1 be 1 rather than x2 be 1?
Yes, you can
Thank you for making life easier 😊😊
Aww you are welcome
Please do laplace transforms for us and thank you in advance
Yes, I will do that
Yes, I will do that definitely
Thank you sir.. Pls what software do you use?
Smooth draw
Please man what software do you use
Hi. I need to know how you simplified that cubid equation to find 3 lambda values
You can combine the factor theorem and the long-division method to obtain the factors of the polynomial. hope you are familiar with the two mentioned above. Especially with the factor theorem, if f(x) is a polynomial of degree more than one and 'a ' is a number, then if f(a) is zero, then (x-a) is a factor of f(x).
Hi i need to know that for long division method for finding the eigen values. What do we divide the equation with?
You just need to use the factor theorem. You put x = a into the cubic function, if it's zero, the x-a is a factor of the cubic function. Which means you already have one eigen value. The you divide the cubic function by the new factor x-a to obtain a quadratic function, then you find it's factors and the corresponding x values
@@SkanCityAcademy_SirJohn thankyou so much
@jaskiratkaur7781 you are welcome
Well done sir
Most welcome
Where do you watch me from?
Goated 🐐
Thank you very much
Wonderful sir.
Thank you very much
Why do you change the rows?
this is because, according to the rule for reduced row echelon form, whenever there is a zero row (a row with all zeros), it must be placed at the last row, hence we interchanged the rows.
@@SkanCityAcademy_SirJohn alright. Thanks