Linear Independence

Рет қаралды 534,833

5 жыл бұрын

We need to be able to express vectors in the simplest, most efficient way possible. To do this, we will have to be able to assess whether some vectors are linearly dependent or linearly independent. How can we make sure that vectors are linearly independent?
Script by Howard Whittle
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Пікірлер: 215

@ProfessorDaveExplains 3 жыл бұрын

Sorry everyone, the first checking comprehension should be linearly dependent, that's my fault!

@carlitobrigante9740 3 жыл бұрын

All good man we love you

@jagjitmor7486 3 жыл бұрын

Sir nice explaination

@bmohan5032 3 жыл бұрын

Thank you sir

@bikram_kumar 3 жыл бұрын

Hmm, I thought I did a mistake and checked the answer by finding determinant, and got linear dependent as the answer :) Thanks for the comment.

@akashgautam4254 2 жыл бұрын

you are the absolute best

@gloriass4965 4 жыл бұрын

I'm a sophomore in college. I'm learning linear algebra this time, and it was hard because the professor's lecture at my school was too difficult. I found your channel while I was looking for a supplement, and it was very helpful. Thank you for this. I hope you will continue to make good videos.

@-evda-1993 2 ай бұрын

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@-evda-1993 2 ай бұрын

am i okay?

@-evda-1993 2 ай бұрын

non't notn't off course

@ciprianurea2752 7 ай бұрын

Watching this 3 days before my midterm. Man, you saved my life

@rezomegrelidze7748 5 жыл бұрын

The most useful channel on KZfaq. I can't wait for your videos about English grammar or SAT vocabulary.

@ryanieyoub4870 2 жыл бұрын

Professor Dave, my sweet love. Its people like you that make this life worth living. Nothing I could ever say here could be enough to repay how much you've helped me and countless others. The sheer mass of your contribution to the art of midnight test cramming shakes me to the very core of my being. Truly you have shaped the academic standings and futures of many young lives in this modern world. My feeble words are like specks of dust before your colossal persona of generosity and concise mathematical explanations. Thank you

@danischn6246 Жыл бұрын

A poetic masterpiece

@sanashamsi7405 Жыл бұрын

prof dave!!! a bundle of thanks to you, i wish i could have found your videos before, i am searching for good explanation of vector spaces from last 3 weeks and finally found today. it has literally made me calmer otherwise i was worried about how will i go through my semester exams. the best part of your channel, topicwise short videos with examples, a million times thanks! (you have explained linear transformation in the best way on the whole youtube, even better than my prof). lots of love and good luck!!! :)

@loveconomics 3 жыл бұрын

Once again, Professor Dave pulls through with the best, clearest, and shortest video on the topic.

@gmjmoviereviews8900 2 жыл бұрын

You are doing a great job. I'm a freshman doing Linear Algebra, in Africa. This has been helpful.

@takeoff984 3 жыл бұрын

i watched your videos since freshman in highschool and now I'm a sophomore in college you've always been so helpful man

@memetherapy 3 жыл бұрын

I'm just learning this, but I'm pretty damn positive the answer to the 1st checking comprehension question is linearly dependent. If this was a sly trick to get me to go over determinants and linear dependence, well done Prof Dave.

@ProfessorDaveExplains 3 жыл бұрын

Yeah, that's my bad. You're right.

@maxsfriends6653 3 жыл бұрын

@@ProfessorDaveExplains It legit made me understand it more, because I really questioned myself and went over the material again. You're the best. Thank you!

@Flunkeren Ай бұрын

Thank you for this comment. I was scratching my head and wondering if I had misunderstood something, lol.

@yasinzengin3035 Жыл бұрын

What a great explanations... Thanks a lot Professor Dave!!!

@AbhishekJain-jl3oj 5 ай бұрын

Very informative, your way of teaching is simply awesome. Thanks for your contribution.

@justakizuner6359 2 жыл бұрын

Very nice and useful video. Thanks professor!

@PlayWManu Ай бұрын

question one is linearly dependent since the determinant is 0

@danielmoss7133 3 жыл бұрын

this video is a life saver. Thank you so much!

@perspicacity89 Жыл бұрын

You are a very bright and phenomenal teacher. Thank you so much.

@darshansuresh7054 3 жыл бұрын

I am really finding these videos very helpful. Could you please make some videos on the topic "Mathematical analysis" please?

@amruthap4301 6 ай бұрын

Such a simple explanation thank you so much!

@kennettemaddela5682 2 жыл бұрын

Another math legend to the rescue! Thank you

@NatalieMatz 2 жыл бұрын

Oh wow, this video is great! I spent 6 weeks of the course trying to understand it and this really spoke to me

@loveyourself856 5 ай бұрын

That's what we call a super duper lecture that helps us break through the concepts like nothing... Thank you professor Dave for this wonderful lecture 😊

@ahmednasirabdi6567 5 жыл бұрын

Thanks Mr DAVE keep going

@curtpiazza1688 3 ай бұрын

Great! I'm starting to understand these concepts! 😊

@ramlaaal 10 ай бұрын

best intros ever, very short and right to point.

@user-pv3ov5se8q 2 ай бұрын

best explanation ever! That is so helpful!

@elenachen5146 Жыл бұрын

Man this is so well explained! You are a genius！

@sussyuchiha5780 8 ай бұрын

wonderful explanation prof!

@dabeeramir1407 7 ай бұрын

very well explained video. I'm sick and have a quiz in 2 hours and I was able to clearly understand everything

@nataniosif5626 2 жыл бұрын

You're such a blessing, God bless you!

@SM-yq7oo 2 жыл бұрын

thank you, professor Dave ✌

@christianvelasco4594 8 ай бұрын

I started on this channel back in high school watching your flat earth debunk videos for entertainment, and now here I am watching for supplementation to my college courses. Your videos have been super helpful!

@gamingchannel-es9dh Жыл бұрын

Hey I'm from India I have the course of bachelor of mathematics honours and I'm have found your content great .. 👍👍 thankyou Dave professor 🌹

@vishnuchittanramesh4033 Жыл бұрын

Lovely video, helped me a lot in my Grade 11 exams.

@pasansulakshanarathnayaka3836 Жыл бұрын

Simply & clearly ❤️

@pmrsk1 Жыл бұрын

man you're great teacher trust me my university profs are not able to teach like you

@aditidump 8 ай бұрын

i finally understoodthis love ya prof!

@chethankr3598 Жыл бұрын

Beautifully explained

@Briancheboi-yo7nh 2 ай бұрын

awesome presentation I actually got the point home

@Sanju-199 2 ай бұрын

It make sence 🥹 Thank You soooo much ❤

@mbenitez6722 4 жыл бұрын

Just finished the first comprehensive question and it should be linear dep, i tried switching the vectors around in case i got it confused and i still got the det=0

@pawanpratap3930 3 жыл бұрын

Yeah you r right. I also found it linearly dependent by both method.

@mahad596 3 жыл бұрын

You are right

@MohamedAshraf-vh3jo 3 жыл бұрын

Same here 🤚

@srijanjha7850 2 жыл бұрын

Yeah i also found the same it might be a typo .

@immortalspiritualbeing7037 2 жыл бұрын

I got the same answer

@MildSatire Жыл бұрын

You're an absolute legend

@HWFieldGoal 2 жыл бұрын

Best lecture thank you!!!

@gesakanancy6165 7 ай бұрын

Wow, that is really anice video, I have learnt alot from your video, keep it up

@nilskuhna3320 3 ай бұрын

thanks, needed this

@asif7240 Жыл бұрын

Thank you so much!

@monkww 6 ай бұрын

U r literally a life saver

@vichitrakumar4452 2 жыл бұрын

Great Video!!

@andressd2405 2 жыл бұрын

Thanks!

@Daani213 2 жыл бұрын

Thank you so much .

@wesselbeer8041 Жыл бұрын

the linear independence of the polynomials were the only thing I skipped of this whole playlist. guess what came on my test today :') always watch the whole Professor Dave Explains video kids

@myjapanesejourney7344 3 жыл бұрын

Professor Dave, please do something to let people know that the first comprehension question should actually be linearly dependant as it really confused me. Thank you so much.

@bao5860 5 жыл бұрын

the first question in checking comprehension shouldn't be linearly dependent since the determinant is zero?

@antonholm114 4 жыл бұрын

Yeah it is linearly dependent, also = + 2.

@bernab 4 жыл бұрын

@@antonholm114 I think so. I made calcultations and the determinant was -5+10-5, so, it means 0. 3 linearly dependent vectors.

@tella5357 3 жыл бұрын

@Mostafa AL Fatih lmao

@mahimmarufuzzaman3588 3 жыл бұрын

Yes, it is Linearly Dependent. I checked both row reduction and determinant method.

@stradok4106 Жыл бұрын

I had also stumbled upon such concepts. You see the thing is a matrix having a trivial solution means that on putting the unknown in the linear eq we should get zero so Ax=0 but in case of a determinent there are no unknown variables an determinent is purely of enteries of a so both have different results Having a non singular determinent means that this matrix has linearly independent coloumns as there is a property that states if any two coloumns of a matrix are identicle in any way then |A| = 0

@missakasms 8 ай бұрын

thank you professor dave

@EsotericBibleSecrets 5 жыл бұрын

Hey Dave, which do you think is the most accurate for the way the universe will end? Big Rip, Big Freeze, etc

@ProfessorDaveExplains 5 жыл бұрын

I think the rip, but we still don't know what dark energy is so that could very well change.

@samiafarah3931 2 жыл бұрын

thank yu sooooo much teacher great job

@bananewane1402 3 жыл бұрын

Thank you Dave. This helps me a lot 😊

@mst.shekhakhatun179 5 жыл бұрын

Thanks

@adefisanadedotun797 Ай бұрын

Thank you

@3amvortex Жыл бұрын

THANK YOU!

@KovelamudiSriChandanaAP 3 жыл бұрын

Thank you Sir

@tshegofatsomaepa4827 Жыл бұрын

You are the best proff

@anujintseweendorj5829 6 ай бұрын

love your videos

@justthenamekevin 2 жыл бұрын

thank you i didn’t understand anything and failed my exams before i found this playlist!!!!

@happyevening2322 9 ай бұрын

thank you sir you taught in 15 minutes what my professor did in 4 hours

@AaromGuillaume-er8pe Жыл бұрын

This video ended my professor's whole career. Big W!!!

@JulioCesar-nq8fv 3 жыл бұрын

YOU ARE A LIVE SAVER, i've being reading my text book for like a week trying to understand vector space and this stuff but just watching your videos taught me so much, thank you so much dude

@pradeepreddy3317 3 жыл бұрын

In the 2nd comprehension question should the vector be written in vertical or horizontal positions to solve elementary row operations? I mean 4*3 matrix or 3*4 matrix to start solving?

@CHEESYhairyGASH 2 жыл бұрын

I wrote them vertically. First time I did it I got linearly independent, second time I tried again after going to this video: kzfaq.info/get/bejne/ibWqgpx2yLfIgZc.html I got linearly independent the second time around, but it took 11 rounds of elementary row operations.

@user-nz6nz9zf5e Жыл бұрын

Iam from Egypt...thank you for your explanation ❤❤

@ms_1918 4 жыл бұрын

Best video

@krishnabharadwaj7312 7 ай бұрын

Can anyone explain how the checking comprehension's second question is Linearly Independent, After row reducing it into its echelon form im not getting an Identity matrix . Any help is greatly appretiated !!

@Flunkeren Ай бұрын

This is the matrix you get from combining vectors a, b, c: [ 1, -1, 2] [ -3, -1, -2] [2, 2, -3] [1, 5, 3] Done right, row reducing that matrix will eventually give you: [1, -1, 2] [0, 1, -1] [0, 0, 1] [0, 0, 0] So, writing that up with scalars and equating to zero, we get: c_1 - c_2 + 2c_3 = 0 c_2 - c_3 = 0 c_3 = 0 Inserting c_3 into the first 2 equations, you will get: c_1 = 0 c_2 = 0 c_3 = 0 This makes the vectors linearly independent.

@zaidazim6128 4 жыл бұрын

Isn't the answer to the first comprehensive question linearly dependent? The determinant being 0.

@mkacademy3908 2 жыл бұрын

kzfaq.info/get/bejne/ecePfKeZtLicZmw.html Linear Independence and dependence of vectors

@SM-yq7oo 2 жыл бұрын

@@mkacademy3908 hello! how are you?

@arsojib Жыл бұрын

yes

@President_Starscream 5 жыл бұрын

I think I sprained my brain trying to keep up.

@coolbe07 9 ай бұрын

7:41 i dont get it. This matrix is still going to be linearly independent though its last row is all zeros? And it is independent because we can see that all of the terms (I mean c1, c2, and c3) are equal to zero?

@seungwanhong3689 2 жыл бұрын

I was watching his video 2 years ago when I was working on Undergrad courses, and I am in Grad school now still watching his videos. I love this Jesus looking dude. DAmen!

@user-ef2pl4hz8l 6 ай бұрын

second comprehension is also linearly dependent? Since there are 3 equations and 4 unknowns , even if we get leading 1 in all the rows, there will be one free variable....hence the vectors are linearly dependent....this goes without solving or reducting the matrix. Is my understanding correct? Kindly respond

@anitb1874 5 жыл бұрын

Awesome

@manoj_n9575 3 жыл бұрын

Thank u sir

@vuwla 3 ай бұрын

Interesting explanation, different from the typical explanations in engineering mathematics classes. This video is definitely easier to understand but seems lacking in the number of theorems covered

@vuwla 3 ай бұрын

It would be really nice if you could apply this easy explanations on a wider range of thopics and deeper level, it would help many crash their maths courses completely!

@idnenekd94 Жыл бұрын

thankyou sirr

@christianahaloba3255 Жыл бұрын

How did the first illustration change from a+2b to 2a+b I thought b was the one with the coefficient of 2 and not a

@emilyireland3726 3 ай бұрын

Thanks king

@thehgamers 4 ай бұрын

in the test your comprehension by determinant method, determinant is zero so its linearly dependent but video says otherwise..can someone explain?

@lux4019 Жыл бұрын

Unsure if you still check comments on these videos, but in the example where you added 3 length 4 vectors together could you also add another length 4 vector with the value (0,0,0,0) in order to construct a square matrix then find its determinant to see if the 3 vectors are linearly independent?

@nativitymeldmacunat7163 Жыл бұрын

hi, i don't think so. a matrix with a column of zeros will always have a determinant equal to zero, but it is possible to have 3 linearly independent vectors (even though they are all of length 4). whenever you don't have a square matrix, you'll have to solve it through elementary row operations. :')

@AamirSiddiquiCR7 2 жыл бұрын

Professor Dave, the first homework question's answer is zero when solved using determinant method, then it should be Dependent and NOT Independent

@AzaanKhan-dx8rw 3 жыл бұрын

Thanks.

@crazygur1y Жыл бұрын

tysm

@ziyuzhou-vt2wx 5 ай бұрын

amazing

@imsaad2514 2 жыл бұрын

First time taking your lecture from Pakistan and love u ❣️❣️

@CHEESYhairyGASH 2 жыл бұрын

Hi there, would it be possible to have a solution for the second comprehension question. I worked through the question 3 times and every time I get linearly dependent.

@CHEESYhairyGASH 2 жыл бұрын

Ok I tried it again and got linearly independent.

@OldHunter_blaidd 7 ай бұрын

@@CHEESYhairyGASH how?? I tried to solve it in multiple ways and always get linearly dependent, i always end up with 3 equations but 4 unknowns -> free variable -> linearly dependent Plz answer as fast as possible as i have an exam tomorrow 😅

@hunorcsenteri3775 3 ай бұрын

What if lets say c1= any number other than 0, like 1. If c1=1, it is independent of any other cs, but it is not 0. Does this mean it is independent?

@sagarkakkar5716 3 жыл бұрын

sir in checking comprehension 1st question is linearly dependent

@AhmedMohamed-wi5pu 5 жыл бұрын

prof please did you finish the calculus series ? thanks in advance

@ProfessorDaveExplains 5 жыл бұрын

yes i did, on to other topics!

@AhmedMohamed-wi5pu 5 жыл бұрын

@@ProfessorDaveExplains should i watch it before the modern physics series and what is your advice for me to get better in it ? and again thanks for the great effort Mr Dave

@ProfessorDaveExplains 5 жыл бұрын

hmm well i didn't include almost any math in my modern physics series so you can definitely watch those right away, i may learn more physics at a later date and do more rigorous tutorials on those subjects at that point.

@bimini8425 6 ай бұрын

does anyone have a solution for the second comperehension exercise? pls help!

@abnerandreymartinezzamudio3366 2 жыл бұрын

Simplicity is the most elegant form of complexity

@vnky01 3 жыл бұрын

After sometime my brain, He knows a lot about science stuff professor dave explains [flute bgm rolls]😂😂😂

@elvykamunyokomanunebo1441 2 жыл бұрын

Hi professor, @7:14 we could end up with 2 equations with 3 unknows, as you've stated, however, if we take an extra step --> R1 = R1 + R2 this will lead to: [[1, 0, 7/2], [0, 1, 3/2], [0, 0, 0], [0, 0, 0]] It's not clear why you didn't take the extra step. I tried it out in Python and the output is as above and it shows that column 1 and column 2, vectors, are the only linearly independent columns(vectors). but above, in solving the system of equations you've not specified which of the vectors are linearly independent . Have I mis-understood the interpretation here? Thanks in advance. Elvy

@rexatoedmundson2581 9 ай бұрын

Hi Prof. Please I think the exercise you gave at the end of the video is supposed to be be linearly dependent for the eg. 1

@k_nito7954 8 ай бұрын

yeah, its linearly dependent, see the pinned comment on this video

@krishaaswani4651 Жыл бұрын

What if one of the variables in the matrix does not have a value. For example, you are trying to find which of the following vectors are linearly independent: c1 (1, a, 0) + c2 (a, 0, 1) + c3 (0, 1, a)

@inxendere Жыл бұрын

You simply put it as a 0 in the matrix and solve