🔷15 - Eigenvalues and Eigenvectors of a 3x3 Matrix

[@evansokosodo2791]

This is so straightforward. What a good teacher! Many thanks.

[@SkanCityAcademy_SirJohn]

Awww thanks so much

[@azizb.tapeing9249]

So amazing teacher explained clearly. Can I request a lecture on complex root and equal root

[@bitmesrassdsddddsa]

Thanks for existing man

[@SkanCityAcademy_SirJohn]

Thanks be to God

[@percyarthur5556]

16:03

[@SkanCityAcademy_SirJohn]

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.

[@peridakingani]

Understandable 😊

[@SkanCityAcademy_SirJohn]

@peridakingani thanks so much

[@mr2seis388]

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!

[@SkanCityAcademy_SirJohn]

You are most welcome, keep watching for more great content. I really appreciate your comments. Where do you watch me from?

[@petrkasanda4511]

Thanks very much for this teaching Much love ❤ and respect from zambia 🇿🇲🇿🇲🇿🇲

[@SkanCityAcademy_SirJohn]

Thanks so much, Kasanda, I appreciate it. Kindly text me on [phone] whatsapp

[@kwabenablessed4888]

Very clear explanations. This was very helpful. Thank you

[@SkanCityAcademy_SirJohn]

You are welcome

[@tomasito_2021]

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!

[@SkanCityAcademy_SirJohn]

Thanks so much. Kindly check this playlist kzbin.info/aero/PLInywrvFyvq7oAlPscVnXsd8CRTsh0b77

[@D17D]

Thanks for this. You are explaining directly from your heart, with care and love

[@SkanCityAcademy_SirJohn]

Thanks so much for watching, best wishes

[@humzaqureshi1391]

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]

how do you know what to divide by?

[@SkanCityAcademy_SirJohn]

@DevourOrGetDevoured please kindly state the time in the video so I help you out.

[@DevStuf]

@@SkanCityAcademy_SirJohn found out why alr

[@gbgfgfc]

YEP

[@andifrkh]

@@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

[@ibrahimjacksson]

After this video now i can solve eigenvalues and eigenvectors with 3, 3 matrices......Thanks mr✅

[@SkanCityAcademy_SirJohn]

Great

[@OmadiEmmanuel-qx7er]

Number one idea to my coursework,big up tutor

[@SkanCityAcademy_SirJohn]

Great... Thanks so much

[@ftsw7758]

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.

[@Warchler]

It 65, no 63, so it will be 1-24+65-42 which equals 0

[@ftsw7758]

@@Warchler got it. Thanks..!

[@SkanCityAcademy_SirJohn]

It's 65 and not 63.

[@SonnyTechAcademy]

Thanks man. Well explained....the video is long but it's worth it :)

[@SkanCityAcademy_SirJohn]

Thanks so much

[@MulindwaAbdallahconc-sh4ct]

What a good teacher so precise

[@SkanCityAcademy_SirJohn]

Thanks so so much

[@Salamanca-joro]

Absolute cinema! i have final exam on Tuesday and you just saved me

[@SkanCityAcademy_SirJohn]

Aww I guess that's a great feeling for you.

[@Sylviadaniel]

This is the best channel ever God bless you ❤

[@SkanCityAcademy_SirJohn]

Amen. And good luck

[@SainKampila]

now making sense indeed thank you a lot

[@SkanCityAcademy_SirJohn]

You are most welcome

[@yahyadiaa9679]

You saved me from failing my exam for the 4th time

[@SkanCityAcademy_SirJohn]

Wow, that's great

[@plantmc9319]

Dang 4 times that’s crazy. Fr though this dude has the best explanation

[@saja_22A]

How did you get out? Lamda? Final output ? ​@@SkanCityAcademy_SirJohn

[@smshahoriarsomudro3120]

how dull you guy are!

[@palmershot2779]

I've got a test today and this is all. I needed

[@SkanCityAcademy_SirJohn]

That's great. Best wishes

[@yourfriend809]

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

[@SkanCityAcademy_SirJohn]

Aww thanks so much

[@ai_enthusiast86]

amazing teaching method

[@SkanCityAcademy_SirJohn]

thanks so much for your comment. And good luck in your academics

[@helifonseka9611]

Thank you from Sri lanka! 🙏

[@SkanCityAcademy_SirJohn]

Youre most welcome

[@ace09wrld]

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)

[@SkanCityAcademy_SirJohn]

Thanks so much for input❤️❤️

[@DhruvPatel-b9h]

Best teacher ever you are GOAT.

[@SkanCityAcademy_SirJohn]

Aww... Thanks so much. Keep watching for more

[@OpareAddoNanaYaw-tg8ni]

At 28:04 why was (-10-10) equal to 0. If I’m not mistaken it should be 20. More clarity on this please

[@SkanCityAcademy_SirJohn]

R2-R3. -10-(-10) = -10+10 = 0

[@OpareAddoNanaYaw-tg8ni]

@@SkanCityAcademy_SirJohn thanks

[@SkanCityAcademy_SirJohn]

You are welcome

[@Hey99-i7v]

Thank u from my country to your county 💰

[@SkanCityAcademy_SirJohn]

You are most welcome

[@darcash1738]

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]

Wow, really

[@darcash1738]

@@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]

yes actually@@darcash1738

[@SkanCityAcademy_SirJohn]

where do you watch me from? which program do you read and level?@@darcash1738

[@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 😅

[@paulowiredu7586]

From your accent, I could spot you're my Ghanaian brother..... Watching your video from the States. .

[@SkanCityAcademy_SirJohn]

That is correct. I'm a Ghanaian

[@SkanCityAcademy_SirJohn]

That's great, are you doing postgrad studies?

[@perdehurcu]

Kardeşim çok teşekkür ederim. Harika bir ders. Çok basit olarak anlatmışsın. Tebrik ederim.

[@SkanCityAcademy_SirJohn]

thanks so so much

[@chaimaahidji]

this lesson is very awesome , thanks so much ☺

[@SkanCityAcademy_SirJohn]

You are most welcome

[@bobrobert8684]

Excellent tutorials. Thank you.

[@SkanCityAcademy_SirJohn]

You are most welcome, and good luck

[@rivieraokapi]

Thank you my friend, you made it a lot more digestible. What a teacher!!

[@SkanCityAcademy_SirJohn]

You are most welcome. Please keep watching for more

[@scenicsceneBD]

It’s to much helpful, love you man ❤❤

[@SkanCityAcademy_SirJohn]

Thank you so so much

[@Twilightaria]

Godddd bless youuu I've been struggling the wholeee day to understand thisss❤❤❤❤❤❤

[@SkanCityAcademy_SirJohn]

That's great, thanks you got sorted at the end. Where do you watch from?

[@Twilightaria]

@@SkanCityAcademy_SirJohn UAE 🇦🇪

[@SkanCityAcademy_SirJohn]

@idontcare7667 that's fine, im from Ghana 🇬🇭.

[@SkanCityAcademy_SirJohn]

@idontcare7667 Muslim or Christian?

[@cxndy_mocha8076]

This is so easy after listening to this. Tysm! 😭

[@SkanCityAcademy_SirJohn]

Thanks so much for your comments and good luck in your studies.

[@wangster331]

Masterpiece. Writing my exam this morning. It sure would save me 😊

[@SkanCityAcademy_SirJohn]

Yes please, good luck

[@wangster331]

@@SkanCityAcademy_SirJohn thanks, I love you

[@SkanCityAcademy_SirJohn]

@wangster331 aww thanks so much Where do you watch from

[@wangster331]

From Nigeria

[@SkanCityAcademy_SirJohn]

@wangster331 great

[@nelsonanthony9898]

17:33 why do you pick an arbitrary value for x2 but not x1? Will or does it make any difference?

[@SkanCityAcademy_SirJohn]

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.

[@viktordowa]

But if there is a negative it will definitely affect your answer, won’t it?

[@SkanCityAcademy_SirJohn]

@viktordowa please a negative where

[@fediMbf99]

Please how you found lambda with third equation like in the video (10:32)

[@SkanCityAcademy_SirJohn]

It's a cubic equation, just punch on your calculator

[@edsonsimbaya1993]

Thanks, this is very simple explanation

[@SkanCityAcademy_SirJohn]

You are most welcome

[@cherrybuff5991]

Thank you from India♥

[@SkanCityAcademy_SirJohn]

You are welcome

[@selly0072]

God richly bless you🙏🏽

[@SkanCityAcademy_SirJohn]

Amen... thank you very much. best wishes

[@sajjalsayjal3640]

How we find these eigen values that you write??

[@yosraal3mri379]

How can we find the eigen values by calculater??

[@norgac9103]

Excellent explenation. But one point. How i get lamba 1,2,21 without calc ?

[@SkanCityAcademy_SirJohn]

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

[@norgac9103]

​@@SkanCityAcademy_SirJohn And if i cant use calc i must use cubic equation or is there another variety ?

[@SkanCityAcademy_SirJohn]

@@norgac9103 you can use the factor theorem

[@norgac9103]

Thank you .

[@norgac9103]

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

[@KadmielAcquah]

16:53 For lamda 1 ,i think the matrix was not in its row echelon form,if it was can u explain further??

[@SkanCityAcademy_SirJohn]

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

[@stevenkanguya5087]

THANK YOU VERY MUCH,,, YOU JUST EARNED YOURSELF A SUBCRIBER

[@SkanCityAcademy_SirJohn]

thanks so much Steven

[@lauren3441]

When solving for lambda 3, column 3 row 3 isn’t it supposed to be -20? 28:40

[@SkanCityAcademy_SirJohn]

No please, it's -10-(-10) = -10+10=0

[@habib97se]

thank you for the video, you helped med a lot.

[@SkanCityAcademy_SirJohn]

You are most welcome

[@nocapper5002]

Does the order in which you choose the value for lambda matter?

[@SkanCityAcademy_SirJohn]

No please, the order doesn't matter

[@everything4editing.]

Thanks so much ❤❤❤

[@SkanCityAcademy_SirJohn]

You are most welcome

[@JosephOtieno-zu2rm]

I think you need an oscar award🥳🥳🎉

[@SkanCityAcademy_SirJohn]

Thanks so so much

[@masked_man7745]

Explanation is very good and clear. Keep it up.

[@SkanCityAcademy_SirJohn]

Thank you so much

[@masked_man7745]

@@SkanCityAcademy_SirJohn one of these questions came during my exams and I was able to attend it thankyou

[@SkanCityAcademy_SirJohn]

Aww you are most welcome.

[@rizwann098]

Love from Kashmir 🍁❤️

[@SkanCityAcademy_SirJohn]

Thanks so so much

[@rizwann098]

@@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

[@SkanCityAcademy_SirJohn]

@rizwann098 you are most welcome

[@OdongoKizito]

Thank for the wonderful explaination

[@SkanCityAcademy_SirJohn]

Most welcome

[@nesaaqlimakhan]

hey , so for the values of eigenvector , our aim should be making R3 to 0 ?

[@SkanCityAcademy_SirJohn]

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.

[@LPadillaCR]

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]

Hahahah thanks so much, and nice meeting you.

[@allstar7778]

Any reason why you are not using krammer's rule which is much simpler than using charachteristic polynomial equation ?

[@SkanCityAcademy_SirJohn]

No reason please, you can use crammer's to solve as well.

[@allstar7778]

@@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 ?

[@MahmoudIbrahimMohamedIbrahimEl]

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

[@SkanCityAcademy_SirJohn]

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

[@mahmoudelmolla3153]

@@SkanCityAcademy_SirJohn thanks man i appreciate it you are the best

[@SkanCityAcademy_SirJohn]

Thanks so much, El Molla

[@efosaomoregie5246]

Thank you bro we love and appreciate you

[@SkanCityAcademy_SirJohn]

You're welcome

[@SkanCityAcademy_SirJohn]

Thanks for watching

[@Capablemindstutorials]

Thank you sir.. Pls what software do you use?

[@SkanCityAcademy_SirJohn]

Smooth draw

[@BADURELGADIR-dd2ck]

thank you for your useful lecture.

[@SkanCityAcademy_SirJohn]

thanks so so much....I'm grateful

[@ChidiebubeAli]

For the first eigenvalue, I thought it should not have zero as a value​@@SkanCityAcademy_SirJohn

[@viktordowa]

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

[@SkanCityAcademy_SirJohn]

Not necessarily, but if there appears a zero row, then it should be at the button

[@LeftArmMemes]

Why aren't you monetized? Also your method of teaching is soo good.

[@SkanCityAcademy_SirJohn]

Thanks so much

[@FatawYakubu-908]

Please for the cubic equation if u get the values to be decimals, How do we solve it

[@SkanCityAcademy_SirJohn]

Usually you will get whole number values, if you get decimals, kindly check if the cubic equation is right

[@FatawYakubu-908]

@@SkanCityAcademy_SirJohn okay thanks

[@nyambemukena5318]

How did you jump to 21 as the value lambda

[@SkanCityAcademy_SirJohn]

Those are the roots of the equation

[@nehemiahbalozi5731]

Well understood... Thanks

[@SkanCityAcademy_SirJohn]

Most welcome

[@samaawagih7272]

Spectacular Explanation.

[@SkanCityAcademy_SirJohn]

thanks so much Wagih

[@AbbSalehi]

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

[@Zyscha]

For Lambda= 21, my eigenvectors are coming out to be [6,6,1]. Can you please check yours once? I think you can not perform a row operation using a row if you have operated on that same row in the same step.

[@SkanCityAcademy_SirJohn]

Hi Zyscha, kindly check your approach one more time, if you are still not getting what I had, then you let me know, because what I've done in there is the actual thing. Thanks so much

[@Zyscha]

@@SkanCityAcademy_SirJohn I don’t know I have done it multiple times, I reach the same answer. How do I show you my approach?

[@SkanCityAcademy_SirJohn]

Please are you on WhatsApp?

[@akhileshakhil4390]

how did you get the roots of the equation, I mean how did you get the eigen values.

[@SkanCityAcademy_SirJohn]

I used a calculator.

[@manuelmakritos]

Wow .....I love this explanation

[@SkanCityAcademy_SirJohn]

Thanks so so much

[@kabzofficial2142]

Why did you leave out 3 when finding for Row one

[@SkanCityAcademy_SirJohn]

Can you please elaborate more

[@kabzofficial2142]

@@SkanCityAcademy_SirJohn oh no I was just confused on why you were swapping the roles and then multiplying the other rows and what not yeah

[@SkanCityAcademy_SirJohn]

Okay, when converting to the row echelon form you can swap rows. That is a rule to that effect. Kindly watch video kzbin.info/www/bejne/pIfWnWikltmXrqc

[@samuelwani6093]

Appreciate your lecture sir

[@SkanCityAcademy_SirJohn]

Amen and thanks

[@calvinbasotho8437]

Hi. I need to know how you simplified that cubid equation to find 3 lambda values

[@SkanCityAcademy_SirJohn]

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).

[@brianomarion]

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?

[@SkanCityAcademy_SirJohn]

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 kzbin.info/www/bejne/apyyo558hMt2qqs

[@brianomarion]

@@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

[@SkanCityAcademy_SirJohn]

Youre welcome

[@pianolessonswithbless879]

You'll test factors of 42 only...Both positive and negative numbers

[@miracle_winter6118]

I'm confused....so is it the same for all examples or the swapping and multiplication will vary? Like.....how do you know what to do? Is the bottom row always supposed to have all 0s?? I'm confused...😢

[@SkanCityAcademy_SirJohn]

It varies, it depends on the question you are solving. The idea is, if there is a zero row, then it should appear at the bottom.

[@kingszedu9060]

Why do you change the rows?

[@SkanCityAcademy_SirJohn]

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.

[@kingszedu9060]

@@SkanCityAcademy_SirJohn alright. Thanks

[@ssalijovan123]

Bless you, but so you have any videos about vector spaces and spaning a vector.

[@SkanCityAcademy_SirJohn]

Amen. No please

[@shivanikumari680]

Can you tell me how to find eigen value of this equation x^3+25x^2+50x-1000 ????

[@SkanCityAcademy_SirJohn]

The eigenvalues are -20, -10 and 5. Use the factor theorem to do so.

[@kubabak4]

I have a 3x3 matrice [57 0 24, 0 50 0, 24 0 43] and all calculators and solutions indicate that the +-+ doesn't apply. I was wondering why could this be i.e. to get the right answer you must solve it with the negative : : (57-x)(50-x)(43-x) -24(50-x)(24). I expected it to be positive. Any idea why ?

[@SkanCityAcademy_SirJohn]

Are you sure you have punch in the calculator the right entries?

[@kubabak4]

@@SkanCityAcademy_SirJohn So the issue was that I ignored the 0s therefore it was +24[(0x0)-(50-x)(24) instead which is non-intuitive.

[@SkanCityAcademy_SirJohn]

Okay

[@georgeasabre6393]

You be doing the most 💪🤲

[@SkanCityAcademy_SirJohn]

thanks so so much. good luck today

[@Dfw_law]

Pls what are we to make 0 Howmany of the values

[@SkanCityAcademy_SirJohn]

Can you please come again? I don't get your question

[@jaskiratkaur7781]

Hi i need to know that for long division method for finding the eigen values. What do we divide the equation with?

[@SkanCityAcademy_SirJohn]

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

[@jaskiratkaur7781]

@@SkanCityAcademy_SirJohn thankyou so much

[@SkanCityAcademy_SirJohn]

@jaskiratkaur7781 you are welcome

[@annahkerubo6371]

In finding eigen values of 21, why did we use row two as the pivot row for reduction and not row 1

[@JonathanTetteh-i6m]

answer this question

[@InthipornBunkhan]

My textbook said λI - A and your is A-λI. Is these two method have a different answer? Because at the start I use λI-A but the rest I follow your method.

[@SkanCityAcademy_SirJohn]

Well you can solve more questions with that approach to see if the answers will be the same, but then my method is what you see in most textbooks.

[@SABRINAHAMID-ok3cz]

THANKS A LOT

[@SkanCityAcademy_SirJohn]

You're welcome!

[@raghavyadav6121]

your videos are really helpful for calculus and linear algebra, thank you!!

[@SkanCityAcademy_SirJohn]

You're most welcome. And thanks for your kind words too.

[@danielkadima571]

with another 3x3 matrix I found the characteristic polynomial, I put the equation which was cubic into the calculator. This way is still difficult to find the eigen values unless I am doing this wrong. So I took the same equation and plugged it into Mathway I found that the roots are decimals?

[@prosperchidexogbodo5386]

Instead of doing that just factor your rh values

[@mcnosike7935]

Thank much for this video it really help

[@SkanCityAcademy_SirJohn]

You're nost welcome

[@MORINGELOMANYAKI]

Nice and reasonable solution

[@SkanCityAcademy_SirJohn]

Thanks so much

[@حسامدوحي]

Think you sif❤❤

[@sanketkumbhar]

How to find eigen values & eigen vector corresponding to smallest eigen value in 3 by 3 matrix

[@sanketkumbhar]

Plz give me thise question answer

[@garpthehero3221]

god bless you thank you so much

[@SkanCityAcademy_SirJohn]

thanks so much

[@Flowers768]

What I should do if this question is part of an exam and this is just Q1 and Q2 are 8 questions of integration and Q3 is a reduction integration and the exam only has 50 minutes and I’m not allowed to use the calculator?

[@SkanCityAcademy_SirJohn]

Wow. You just need to practice constantly. That would help you to be swift in calculating it.

[@Flowers768]

Thank you so much for your help

[@زهرةالخريف-ن9ض]

Thank you very much

[@SkanCityAcademy_SirJohn]

You are most welcome

[@segunpeter5888]

How did u get 21 in the eigen value sir

[@SkanCityAcademy_SirJohn]

Just use a calculator to evaluate the cubic function to get the roots. Or you can use the factor theorem to do so.

[@Enthub47]

Please can you tell me what app you used for this tutorial. The board and pens style in particular. It’s soo smooth 🙂

[@SkanCityAcademy_SirJohn]

I used smoothdraw

[@Enthub47]

@@SkanCityAcademy_SirJohn no wonder it’s smooth ! You do all 🙌🏾🙌🏾

[@SkanCityAcademy_SirJohn]

Thank you

[@watsonnampon2993]

please could you show how to obtain 21 as the eigen values

[@SkanCityAcademy_SirJohn]

You can basically use a calculator, of the factor theorem

[@VirginiaNjeri-o5g]

Thank you!🙂

[@SkanCityAcademy_SirJohn]

You're welcome, where do you watch from?

[@VirginiaNjeri-o5g]

@@SkanCityAcademy_SirJohn I am from Kenya.

[@SkanCityAcademy_SirJohn]

That's great, thanks for watching

[@NamukoseMariam-e5r]

would like to teach me an easy method for getting the eigen vectors than eclon because I have failed to understand

[@SkanCityAcademy_SirJohn]

Really. Sorry about that

[@YasabnehAddisu]

its so tebeda thanku

[@SkanCityAcademy_SirJohn]

You are most welcom