Linear Independence

[@ProfessorDaveExplains]

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

[@carlitobrigante9740]

All good man we love you

[@jagjitmor7486]

Sir nice explaination

[@bmohan5032]

Thank you sir

[@bikram_kumar]

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]

you are the absolute best

[@ciprianurea2752]

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

[@areebagulbahar228]

Watching night of exam

[@protz3624]

i have my midterms after 2hr 40 min

[@BaconBearOfficial]

currently walking to mine

[@inconsistenciez]

watching this 31 hours and 57 minutes before my finals

[@gloriass4965]

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]

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

[@-evda-1993]

am i okay?

[@-evda-1993]

non't notn't off course

[@loveconomics]

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

[@ryanieyoub4870]

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]

A poetic masterpiece

[@rezomegrelidze7748]

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

[@gmjmoviereviews8900]

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

[@takeoff984]

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

[@andressd2405]

Thanks!

[@christianvelasco4594]

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!

[@AaromGuillaume-er8pe]

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

[@wesselbeer8041]

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

[@dabeeramir1407]

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

[@mbenitez6722]

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]

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

[@mahad596]

You are right

[@MohamedAshraf-vh3jo]

Same here 🤚

[@srijanjha7850]

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

[@immortalspiritualbeing7037]

I got the same answer

[@bao5860]

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

[@antonholm114]

Yeah it is linearly dependent, also = + 2.

[@bernab]

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

[@tella5357]

@Mostafa AL Fatih lmao

[@mahimmarufuzzaman3588]

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

[@stradok4106]

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

[@kennettemaddela5682]

Another math legend to the rescue! Thank you

[@sanashamsi7405]

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]

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

[@MildSatire]

You're an absolute legend

[@AnimalSyndicate]

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.

[@lookatrobot]

i watched this 2 times then understand not the video but the core concepts n tricks, u saved my grades.

[@zaidazim6128]

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

[@mkacademy3908]

kzbin.info/www/bejne/eZLCeneehLdrbJo Linear Independence and dependence of vectors

[@SM-yq7oo]

@@mkacademy3908 hello! how are you?

[@arsojib]

yes

[@seungwanhong3689]

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!

[@ramlaaal]

best intros ever, very short and right to point.

[@myjapanesejourney7344]

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.

[@President_Starscream]

I think I sprained my brain trying to keep up.

[@gamingchannel-es9dh]

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 🌹

[@loveyourself856]

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 😊

[@pmrsk1]

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

[@PlayWManu]

question one is linearly dependent since the determinant is 0

[@annieworroll4373]

You are really saving my but in my schools curriculum that has things in... strange orders and lacking prerequisites it really should have had.

[@EmeraldEyesEsoteric]

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

[@ProfessorDaveExplains]

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

[@happyevening2322]

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

[@abnerandreymartinezzamudio3366]

Simplicity is the most elegant form of complexity

[@darshansuresh7054]

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

[@maarinahope]

You are the best bro

[@AbhishekJain-jl3oj]

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

[@Syntaxxed]

This explanation is so clear compared to my textbook LA lol THANK YOU!

[@justthenamekevin]

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

[@danielmoss7133]

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

[@ahmednasirabdi6567]

Thanks Mr DAVE keep going

[@vishnuchittanramesh4033]

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

[@perspicacity89]

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

[@KerolosSabry-k7u]

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

[@yasinzengin3035]

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

[@imsaad2514]

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

[@SM-yq7oo]

thank you, professor Dave ✌

[@curtpiazza1688]

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

[@Le.Vi.No7]

Can anyone explain why the co-ef are zero rather than the x's 10:10

[@krishnabharadwaj7312]

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]

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.

[@lightningrodMC]

​@@Flunkerenthe second one of the vector is [ -3, 2, -2]

[@monkww]

U r literally a life saver

[@AhmedMohamed-wi5pu]

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

[@ProfessorDaveExplains]

yes i did, on to other topics!

[@AhmedMohamed-wi5pu]

@@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]

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.

[@justakizuner6359]

Very nice and useful video. Thanks professor!

[@coolbe07]

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?

[@mst.shekhakhatun179]

Thanks

[@amruthap4301]

Such a simple explanation thank you so much!

[@NatalieMatz]

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

[@vuwla]

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]

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!

[@STKeTcH]

Comprehension 1 is DEpendent right?

[@senmonkashonen5875]

Yeh i think so, i just calculated it two times, it is sure dependent

[@ms_1918]

Best video

[@JacquesAsinyo-e5i]

best explanation ever! That is so helpful!

[@vegetaiv9275]

Thank you so much Professor! Super super helpful!!!

[@JulioCesar-nq8fv]

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

[@Briancheboi-yo7nh]

awesome presentation I actually got the point home

[@nataniosif5626]

You're such a blessing, God bless you!

[@kageoni6619]

Thanks sir!!!

[@primerjuniorschool]

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

[@elvykamunyokomanunebo1441]

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

[@sussyuchiha5780]

wonderful explanation prof!

[@chethankr3598]

Beautifully explained

[@aditidump]

i finally understoodthis love ya prof!

[@elenachen5146]

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

[@pasansulakshanarathnayaka3836]

Simply & clearly ❤️

[@SONIKABENGANI-d4k]

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

[@CHEESYhairyGASH]

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]

Ok I tried it again and got linearly independent.

[@OldHunter_blaidd]

@@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 😅

[@pradeepreddy3317]

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]

I wrote them vertically. First time I did it I got linearly independent, second time I tried again after going to this video: kzbin.info/www/bejne/iYDdgGx7mLaXh8U I got linearly independent the second time around, but it took 11 rounds of elementary row operations.

[@sagarkakkar5716]

sir in checking comprehension 1st question is linearly dependent

[@gesakanancy6165]

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

[@Sanju-199]

It make sence 🥹 Thank You soooo much ❤

[@tshegofatsomaepa4827]

You are the best proff

[@Gangadhara189]

1 comprehension checking is linearly dependent.

[@vnky01]

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

[@krishaaswani4651]

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]

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

[@nilskuhna3320]

thanks, needed this

[@erockbrox8484]

You know what my professor taught us? He said, "its a scanner its a scanner" because he couldn't speak English.

[@shariqsaqib4342]

Come-on you don't have have to make fun of him

[@ILoveMaths07]

?

[@rexatoedmundson2581]

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]

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

[@bimini8425]

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

[@missakasms]

thank you professor dave

[@abdullahusama1527]

the question at the end is LINEARLY DEPENDENT

[@abhyudayamehra]

I KNOWWW RIGHT THANKYOU FOR THIS I DOUBTED MY SKILLS FOR 10 MINUTES

[@kangseyeon6155]

What is the answer for the 2nd comprehension?

[@btwiserseitei8891]

I don't know what i am doing wrong as i got linearly dependent for comprehensive q2 as well :(

[@CHEESYhairyGASH]

I couldn't get a 1 in the leading entry in the third row, so put linearly dependent as well.

[@CHEESYhairyGASH]

Tried it again and got linearly independent. Took 11 rounds of elementary row operations though. Not sure if I am doing it correctly

[@daniabdisa2107]

If any collection of vectors includes the zero vector, then the set is linearly dependent. In this case, v4=⟨0,0,0⟩. how can it go with this concept professor?

[@asif7240]

Thank you so much!

[@kaushikn9510]

i tried solving the determinant question to check whether the vectors are linearly independent , after solving i got det as 0 , it is dependent right ?

[@Daani213]

Thank you so much .

[@hunorcsenteri3775]

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?

[@vichitrakumar4452]

Great Video!!

[@ayoubelghazi8918]

how does one solve the 2nd problem in comprehension?

[@laythibrahim1306]

for comprehension check #1 i got det=0 so that means dependent right? what did you get for the determenant?

[@ProfessorDaveExplains]

yeah the first check comp has an error i think

[@anujintseweendorj5829]

love your videos