Linear Transformations , Example 1, Part 1 of 2

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Linear Transformations - Example 1, Part 1 of 2
In this video, we explore the concept of linear transformations in vector spaces. We will introduce the conditions required for a transformation to be considered linear and demonstrate an example of determining whether a given transformation meets these criteria. By applying the properties of linear transformations, we either verify or disprove the linearity of the transformation.
What You Will Learn:
The definition of a linear transformation and its two main properties: additivity and scalar multiplication.
How to apply the properties of linear transformations to vectors.
A step-by-step example of checking whether a transformation is linear by using the definition.
📚 Check out my book: 1001 Calculus Problems for Dummies for more practice!
👍 **If you find this video helpful, please like, share, and subscribe for more math tutorials!
Support My Work:
If you'd like to support the creation of more math content, consider becoming a patron on Patreon: / patrickjmt
#LinearTransformations #LinearAlgebra #MathTutorial #PatrickJMT #Vectors #TransformationProperties #Mathematics #Additivity #ScalarMultiplication #LinearSpaces #Algebra #MathHelp #MatrixTransformations #HomogeneousTransformation

Опубликовано:

29 сен 2024

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Комментарии : 179

@patrickjmt 18 дней назад

Oh my globbins, this video is so old and crusty. The math is good though!

@haseeb1440 14 дней назад

u backk

@danamuise4117 10 лет назад

I wish I could access your brain during my exam

@strivemwadiwa7205 5 лет назад

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@HK-sw3vi 4 года назад

born too early for that kinda bullshit

@davidmurphy563 9 месяцев назад

Nothing like a good snack.

@Saza-z6z 7 месяцев назад

That's creepy....and the fact that m replying commenting on ur comment after 9 years is more creepy

@kennethmandondo517 4 месяца назад

Kkkķ you are right my friend

@CaidenKeller 4 года назад

Helpful. Thank you.

@mikehardy2418 2 года назад

I miss when there were more numbers than letters in math

@idiotrun1997 11 лет назад

Khan Academy for the concept, PatrickJMT for the examples.

@gloriouswingsresearch4206 4 года назад

Are u sure I'm still on Khan's now

@user-rf4vc7mt4d 4 года назад

@@gloriouswingsresearch4206 Bruh this person already graduated and probably has a job now. I don't think he cares anymore

@celeryystick 4 года назад

@@user-rf4vc7mt4d lmao

@mustafasiddiqui8203 4 года назад

Maybe he's dead.

@dhruvpathi941 4 года назад

I don't know why I went to your channel, but I'm glad I did. you have got some great parodies

@OgbedeKamsi 10 месяцев назад

12 years later, still pure gold. Thank you sir

@fortytwo6257 8 лет назад

Thank you! The worst part about linear algebra is getting bogged down with vocabulary and definitions, this was clear and concise.

@nellvincervantes6233 3 года назад

Linear transformations will make your questions add more questions than answers.

@cameronsantiago3155 3 года назад

Exactly.

@annecorrigan5254 9 лет назад

awesome! a million times clearer than how my textbook explains it! thank you!

@patrickjmt 9 лет назад

+Anne Corrigan you are very welcome. come back any time!

@tts6030 9 лет назад

+patrickJMT Thank you so much, I breathe a sigh of relief every time I hear your voice.

@talentedtenager4023 7 лет назад

mam i frm india ...will u be my friend n facebook..my dream to make foriegn friends

@MoVlogs 9 лет назад

what pen do you use ? it makes me happy :) and my friends are also happy when listening to the pen.. plz reply or ill be sad .. :(

@duplitoaejr 9 лет назад

***** Its a black sharpie marker pen.

@vaga8bnd 9 лет назад

+Sir_Sniff-A-Lot Is it exactly that one? urun.gittigidiyor.com/ofis-kirtasiye/sharpie-kalem-siyah-184291062 If it is tell me please i will buy it

@duplitoaejr 9 лет назад

It looks to be the same, just don't use these on a whiteboard since they are permanent markers.

@timc2832 7 лет назад

I'm exposing you

@MuhammadTKhan-re6cz 7 лет назад

wow you became a famous vlogger now

@Mrius86 6 лет назад

Procrastinating my physics homework by doing math homework and procrastinating my math homework by doing physics homework.

@saba8553 Год назад

I found it the best video explaining linear transformation. Although it was uploaded 11 years from now. Thank You.

@Odysseus690 4 месяца назад

Was the best back in those days , he was the GOAT

@rambooo6021 9 лет назад

This video save my life ,, Really appreciate it ,, thanks alot :)

@MrSidd12 9 лет назад

Ramy George *Saved!!

@pierrefabela 7 лет назад

*petty lmao jk!

@Guru-UPSC 5 лет назад

haha

@DasnarkyRemarky 9 лет назад

Oh god, this was driving me insane until i looked at this. Much appreciated.

@kirsten1996girl 7 лет назад

You are my favorite online math help!! However, I noticed you don't have anything on the Kernal and Range of transformation, column spaces, nor the rank-nullity theorem. If it's at all possible for you to make a video about that or just a quick explanation it would be amazing!!

@ipeednurwatr 10 лет назад

This is very easy to understand and everything is presented clearly. Simply amazing! Thank you so much!

@tamzidchowdhury472 3 года назад

I'm taking this class with one of the best professors at my university. But somehow, your explanation still makes a lot more sense to me.

@zyon2tuff386 3 года назад

Yeah I’m taking this in 8th grade and my dad keeps yelling at me 🥲

@ericcartman1168 3 года назад

I'm taking this with a shity college professor

@jadkhalil9263 2 года назад

@@ericcartman1168 you are 9 years old Cartman and go to elementary school

@Eyenn_n 9 лет назад

Hi Patrick. I've been watching your videos and they are extremely helpful. Thank you so much! ---Would you upload more videos on linear transformations such as rotations or shearing?

@patrickjmt 13 лет назад

@27kaylaaa glad that it all helps : )

@adeldzaferi7519 8 лет назад

Are there any examples in which you calculate the kernel and the range of a linear transformation?

@Marcos132132 8 лет назад

Thank you so much man.. YOOU HAVE NO IDEA HOW MUCH THIS VIDEO HELPED HONESTLY. God Bless you

@CheapAndDirty 11 лет назад

I blew off my online differential equations linear algebra class all summer, thanks to you i finished a semester's worth of work in 6 days. well done man

@aladdinkayqubad1645 3 года назад

You were ahead of the game bro!

@muhammadhusnain9183 5 месяцев назад

Somebody watching in 2024?

@giftneokgoete 5 лет назад

So if I join it means I can get special assistant when I ask ?

@patrickjmt 13 лет назад

@KillaTequilla83 no problem : )

@sierrasaursrex 10 лет назад

You've helped me get through every single one of my calculus classes with full understanding. Thank you soooo much!

@bobbysteakhouse7022 5 лет назад

Sorry to break it to you but I don't think the calculus video you wanted

@follklor9976 8 лет назад

thank you man i am study at computer science with lot of confusing things and thanks to you every things going to be better

@the_eternal_student 7 часов назад

How are the a's and b's making up the u and v related to the x and y in problem a)?

@MrFunkyMushroom123 12 лет назад

Hi Patrick, Can you use the theorem T(v)=A(v) to show that whether it is linear or not?

@sarimshehzad9540 4 года назад

let L:Rn belong to Rm be a function if T(0Rn) Is not equal 0Rm, then T is a nonlinear transformation can you help me in this question

@TheRadems 5 лет назад

This man is a blessing to society

@patrickjmt 5 лет назад

well, what a nice thing to say

@chunkitfan2915 4 года назад

If A is a 2x2 matrix such that tr(A)=3 and tr(A^2)=5 , SO HOW TO FIND det(A)

@eggscellentnakafingo5878 4 года назад

Could anyone please help me out with linear transformation? Urgently. I have an assignment

@generatorblue 6 лет назад

Hello! Are you familiar with the term " Linear Fractional Transformation?" Could you please refer me to any book or article where the term has been used before or after 2014? Thank you

@alankuo2023 Год назад

YES i needed this

@tassimamustafa5759 4 года назад

Kinly send me whole topic of linear transformation ....for presentation ....plz

@alaahosn7247 9 лет назад

You're about to save my semester, wish I found these much sooner

@nikhildhoke146 8 лет назад

no.1 explanation

@hrishikeshgautam5 Год назад

Thanks you saved me from failing my upcoming exam in 4 hrs

@eggscellentnakafingo5878 4 года назад

PatrickJMT it would be nice to get help from you

@SincerelyBradley 12 лет назад

your Calc videos got me through the course, so glad you added Linear Algebra ones too!

@YosephAlem2024 2 года назад

this man got me through college

@SincerelyBradley 2 года назад

@@YosephAlem2024 crazy to see this pop up 10 years later. I ended up graduating, getting a masters and having a fairly successful career. this was one of the important stepping stones that got me there. Thank you!

@amzone1274 3 года назад

Damn I'm only seeing this now an I'm jct about to write

@BryceSH1992 10 лет назад

talk about restoring hope when hopeless . i get this now!!!!!

@thomasparris4430 9 лет назад

6:40 "...........thrilling stuff......" hahaha at the sarcastic enthusiasm. I know you probably get burnt out sometimes on every little obscure, mundane, mathematical procedure that you must demonstrate patrick! It's understandable. Thanks for doing this stuff!

@zPoiison 5 лет назад

Good video, everything is well explained etc.. but don't you think you waste too much paper?

@belowaverageasian7197 6 лет назад

Why does part 1 have more than twice the views as part 2??? Did the majority of people get too lazy and decide not to watch the second example??

@quiney_7831 6 лет назад

Hi, How would I go about solving this question: Consider the transformation T : R3 → R3 that projects vectors onto the line l given by x = [0, 0, 0] + t[1, 0, 1], t ∈ R3 (a) Find a formula for T ([ x,y,z ]), and prove that T is a linear transformation. (b) For A the matrix associated to T, describe (justifying your answers) (i) the relationship between row(A) and the line l; and (ii) null(A) as either the trivial subspace {0}, a line through the origin, or a plane through the origin. Thanks!

@vyomraval1999 5 лет назад

I am finding a lot of difficulty to understand these new topics. I have never been through these words like Domain, Function, Vector & many more. Please can anyone make me understand these things & topics. Thank-you:))

@guntashsingh10 6 лет назад

if t and k are two linear tramsformation from V(3)R to V(2)R and V(2)R to V(2)R as t(a,b,c,)=(2a,b+c) and k(a,b)=(b,a) then how tK and kt defined ?

@boydmwansa8750 7 месяцев назад

I was finding difficulties when it comes to linear transformation but thanks I can do this on my own wow just wow!!!

@gloriouswingsresearch4206 5 лет назад

patrickJMT What is the application of the linear transformation? What is the application of transformation that are not linear and can linear transformation be useful for non-linear transformation?

@sarimshehzad9540 4 года назад

please sir solve my problem plz sir its a humble request

@Shokukumi 10 лет назад

Very easy to understand and great if someone has no idea what mapping means. Question: This was a vector transformation. Is a linear algebraic function of f(x) = ax the equivalent of a transformation/mapping with numbers instead of vectors?

@andyhype2546 5 лет назад

Salutations to all Mathers who’ve made it this far. Unless you’re a math major, the end is nigh

@miradc234 8 лет назад

Thank u very much for ur videos... it's really helpful especially ur videos about linear dependent and linearly independent... can i ask u something..? i have problem dealing with these questions... are these linear transformation? T(a1,a2) = (1,a2) T(a1,a2) = (a1,a1^2) Thank u in advance... God bless...:)

@anlerdem3036 8 лет назад

I fall in love with you Patrick, you are so fucking damn bloody amazing!

@k2___2 Год назад

thank you, really helping me out

@siamakghandian 12 лет назад

Hi patrick . how can i find the rest of this video if there is any. Is there any more videos as far as kernels and more linear transformation please. All start making sense to me . thanks to you for your excellent teaching.

@HamzaAli-ht4jc Год назад

The best to understand the linear transformation May God bless you bro

@ZaidAlmymoni 8 лет назад

a1+b1-a2+b2 = a1-b1-a2-b2(the sign defferint - not same +) ?

@ato4900 8 лет назад

if u were righthanded the view would have been much better anyways nice n clear

@WriteRightMathNation 11 лет назад

Good for your precalc ``teacher''! Eventually, you need to learn to learn on your own anyway, by finding resources (i.e. do RESEARCH).

@santiagogonzalezbenjumea9880 7 лет назад

I have been looking for this explanation the whole afternoon on spanish(my mother language) and finally I found it on english, thank you!

@rizzaangelagonzales5282 2 года назад

I have report next saturday, and I was worried because I hadn't found tutorial videos or videos that would help me to understand this kind of topic, but fortunately I have found yours and thank God, finally I understand what Linear Transformation all about is.

@skatinho9883 4 года назад

Ayy these videos aren't monetized? You da legend bro

@killuazoldyck169 4 года назад

okay i get everything in linear algebra but LT i guess not meant to learn it

@laxmanprajapati7101 7 лет назад

alright sir Please upload video to find linear transformation of given kernel

@SorryCrane16 10 лет назад

does it really take that long to determine whether its linear or not /:

@goldfishyzaza5770 11 лет назад

Do you have videos or notes on Euclidean geometry and transformation and affine transformation?

@surajmohan5746 7 лет назад

It's give me lots of thing that i don't know.. Thank u sir

@AK-gt8zy 8 лет назад

Can you please make a video on how to find the transformation matrix?

@IamJacksColon4 12 лет назад

the conditions x-y x-y 2x are they general or did u just make them up?

@MohamedElsheikh22 12 лет назад

Thanks veryyyyyyyyy much.. ربنا يكرمك :)

@AtaTechnicalStudyAta 6 лет назад

Simple and easily tutorials here thanks u

@wesamothman2123 10 лет назад

Thank you very helpful and makes math very easy

@Ansar_Abbas Год назад

Thanks sir its help me for my exam

@amelia20717 5 лет назад

...Has anyone ever told you you sound like David Cross...?

@santoryu8940 7 лет назад

do we not distribute the T? like in 7:19, T([asub1, asub2]), will that not be equal to Tasub1, Tasub2?

@santoryu8940 7 лет назад

so T is the transformation given. ive kinda thought of it as a variable. dammmmmmmmmmmm am i rite guys

@furkantasbasi2789 8 лет назад

can u cover matrix representations as well thanks in advance

@jacksonkundy8573 4 года назад

Thank you Patric...you've made a bunch of Engineers so far.! simple and clear explanations.

@patrickjmt 4 года назад

thanks, i appreciate it :)

@samridhibahuguna7451 4 года назад

Nice explanation...

@berkay6565 11 лет назад

you are really good mannn you have absolutely gorgeous technic.

@pacorta123 Год назад

chatgpt recommended me to watch this video

@ultranoobcodm Год назад

lol as if chat gpt will listen to motherfuckers like you

@vincelunceford 11 лет назад

definitely better than khan academy......thanks so much

@generic7939 5 лет назад

Why's the sound always so low on these vids

@shraddhaprabhakar4365 2 года назад

thank u so much

@SweRaider1993 11 лет назад

Do you have videos on Eigenvalues and vectors as well? :) Thanks!

@tayyab.sheikh 11 месяцев назад

Such a clear explanation ❤

@ZaidAlmymoni 8 лет назад

pleas help, are - and + satisfied?

@astr3. 3 года назад

2020 visitor?

@ghazalabaraki435 5 лет назад

😎 you are a left hander!!!

@rohaanjoshi4809 7 лет назад

thank you so much.. appreciate it.

@ElifArslan-l9g 2 года назад

thank you

@alicependenza4938 3 года назад

patyy booy

@FaizanZahidNustian 11 лет назад

You r awesome, you explain a lot better than others .

@shepherdyannis697 9 лет назад

Much clear than textbook

@smithjane7673 6 лет назад

It’s just so helpful and clear! Thanks a lot!

@gayatrigangurde7937 5 лет назад

Linear operator example sovle

@ImmortalScrub 11 лет назад

Thank you so much for this video. The textbook I was trying to learn this from showed T(U+V) and just assumed that it was equal to T(U) + T(V) without any explanation. I would have been completely SOL without you.

@nellvincervantes6233 3 года назад

You can watch prof dave explained. He has a proof/example on T(U+V) = T(U) + T(V).