Linear Independence

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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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Опубликовано:

15 апр 2019

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Комментарии : 219

@ProfessorDaveExplains 3 года назад

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

@carlitobrigante9740 3 года назад

All good man we love you

@jagjitmor7486 3 года назад

Sir nice explaination

@bmohan5032 3 года назад

Thank you sir

@bikram_kumar 3 года назад

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 года назад

you are the absolute best

@gloriass4965 4 года назад

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 3 месяца назад

i thimk its dogma cuz its dodma cuz its dolma cuz its cuzma

@-evda-1993 3 месяца назад

am i okay?

@-evda-1993 3 месяца назад

non't notn't off course

@ciprianurea2752 8 месяцев назад

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

@loveconomics 3 года назад

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

@ryanieyoub4870 2 года назад

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 Год назад

A poetic masterpiece

@rezomegrelidze7748 5 лет назад

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

@takeoff984 3 года назад

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

@gmjmoviereviews8900 2 года назад

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

@memetherapy 3 года назад

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 года назад

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

@maxsfriends6653 3 года назад

@@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 Месяц назад

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

@sanashamsi7405 Год назад

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!!! :)

@TJBEATSAMV 6 дней назад

Thanks for all the videos on vector spaces ! They really are helpful !!

@kennettemaddela5682 2 года назад

Another math legend to the rescue! Thank you

@yasinzengin3035 Год назад

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

@danielmoss7133 3 года назад

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

@perspicacity89 Год назад

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

@christianvelasco4594 8 месяцев назад

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!

@ahmednasirabdi6567 5 лет назад

Thanks Mr DAVE keep going

@justakizuner6359 2 года назад

Very nice and useful video. Thanks professor!

@AbhishekJain-jl3oj 5 месяцев назад

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

@NatalieMatz 2 года назад

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

@loveyourself856 6 месяцев назад

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 😊

@PlayWManu 2 месяца назад

question one is linearly dependent since the determinant is 0

@ramlaaal 11 месяцев назад

best intros ever, very short and right to point.

@SM-yq7oo 2 года назад

thank you, professor Dave ✌

@MildSatire Год назад

You're an absolute legend

@vishnuchittanramesh4033 Год назад

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

@dabeeramir1407 7 месяцев назад

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

@gamingchannel-es9dh Год назад

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 🌹

@pmrsk1 Год назад

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

@amruthap4301 7 месяцев назад

Such a simple explanation thank you so much!

@nataniosif5626 2 года назад

You're such a blessing, God bless you!

@chethankr3598 Год назад

Beautifully explained

@sussyuchiha5780 9 месяцев назад

wonderful explanation prof!

@pasansulakshanarathnayaka3836 Год назад

Simply & clearly ❤️

@user-pv3ov5se8q 2 месяца назад

best explanation ever! That is so helpful!

@mst.shekhakhatun179 5 лет назад

Thanks

@darshansuresh7054 3 года назад

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

@elenachen5146 Год назад

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

@Briancheboi-yo7nh 3 месяца назад

awesome presentation I actually got the point home

@curtpiazza1688 3 месяца назад

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

@monkww 7 месяцев назад

U r literally a life saver

@Sanju-199 2 месяца назад

It make sence 🥹 Thank You soooo much ❤

@mbenitez6722 4 года назад

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 года назад

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

@mahad596 3 года назад

You are right

@MohamedAshraf-vh3jo 3 года назад

Same here 🤚

@srijanjha7850 2 года назад

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

@immortalspiritualbeing7037 2 года назад

I got the same answer

@wesselbeer8041 Год назад

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

@kageoni6619 11 дней назад

Thanks sir!!!

@HWFieldGoal 2 года назад

Best lecture thank you!!!

@andressd2405 2 года назад

Thanks!

@happyevening2322 10 месяцев назад

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

@asif7240 Год назад

Thank you so much!

@justthenamekevin 2 года назад

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

@aditidump 8 месяцев назад

i finally understoodthis love ya prof!

@AnimalSyndicate 13 дней назад

The formal definition in our uni sucks. The lecturer sucks also too. I went on to work on my degree using the knowledge from this video and it helped me a ton.

@nilskuhna3320 3 месяца назад

thanks, needed this

@Daani213 2 года назад

Thank you so much .

@missakasms 9 месяцев назад

thank you professor dave

@myjapanesejourney7344 3 года назад

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.

@AaromGuillaume-er8pe Год назад

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

@ohsungc2 3 месяца назад

Thank you

@tshegofatsomaepa4827 Год назад

You are the best proff

@vichitrakumar4452 2 года назад

Great Video!!

@KovelamudiSriChandanaAP 3 года назад

Thank you Sir

@3amvortex Год назад

THANK YOU!

@President_Starscream 5 лет назад

I think I sprained my brain trying to keep up.

@gesakanancy6165 8 месяцев назад

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

@user-nz6nz9zf5e Год назад

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

@ms_1918 4 года назад

Best video

@samiafarah3931 2 года назад

thank yu sooooo much teacher great job

@EsotericBibleSecrets 5 лет назад

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

@ProfessorDaveExplains 5 лет назад

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

@JulioCesar-nq8fv 3 года назад

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

@abnerandreymartinezzamudio3366 2 года назад

Simplicity is the most elegant form of complexity

@anujintseweendorj5829 6 месяцев назад

love your videos

@AzaanKhan-dx8rw 3 года назад

Thanks.

@bananewane1402 3 года назад

Thank you Dave. This helps me a lot 😊

@crazygur1y Год назад

tysm

@seungwanhong3689 2 года назад

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!

@bao5860 5 лет назад

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

@antonholm114 4 года назад

Yeah it is linearly dependent, also = + 2.

@bernab 4 года назад

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

@tella5357 3 года назад

@Mostafa AL Fatih lmao

@mahimmarufuzzaman3588 3 года назад

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

@stradok4106 Год назад

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

@imsaad2514 2 года назад

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

@emilyireland3726 3 месяца назад

Thanks king

@anitb1874 5 лет назад

Awesome

@manoj_n9575 3 года назад

Thank u sir

@zaidazim6128 4 года назад

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

@mkacademy3908 2 года назад

ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-Ca_IDhOR868.html Linear Independence and dependence of vectors

@SM-yq7oo 2 года назад

@@mkacademy3908 hello! how are you?

@arsojib Год назад

yes

@sagarkakkar5716 3 года назад

sir in checking comprehension 1st question is linearly dependent

@idnenekd94 Год назад

thankyou sirr

@ziyuzhou-vt2wx 5 месяцев назад

amazing

@user-ef2pl4hz8l 6 месяцев назад

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

@alwaysfax1769 9 месяцев назад

i love you bro..

@coolbe07 9 месяцев назад

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?

@pradeepreddy3317 3 года назад

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 года назад

I wrote them vertically. First time I did it I got linearly independent, second time I tried again after going to this video: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-SOzO9EcQdQc.html I got linearly independent the second time around, but it took 11 rounds of elementary row operations.

@AamirSiddiquiCR7 2 года назад

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

@vuwla 3 месяца назад

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 месяца назад

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!

@ayoubelghazi8918 3 года назад

how does one solve the 2nd problem in comprehension?

@christianahaloba3255 Год назад

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

@krishnabharadwaj7312 7 месяцев назад

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 Месяц назад

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.

@odarfesto367 3 месяца назад

Am just joining my university but am getting there to lecture my lecturer now😂. Thanks Prof

@KyselPoints 2 года назад

SO COOL. Tomorrow is my board exam and i understood this topic today. Thanks a lot professor.

@vnky01 3 года назад

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

@sameerthor11 Год назад

sir can you try the second comprehension question once again

@lux4019 Год назад

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 Год назад

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. :')

@krishaaswani4651 Год назад

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)