Linear Independence

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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[ProfessorDaveExplains]

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

[gloriass]

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.

[ciprianurea]

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

[loveconomics]

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

[ryanieyoub]

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

[memetherapy]

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.

[rezomegrelidze]

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

[takeoff]

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

[gmjmoviereviews]

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

[mbenitez]

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

[PlayWManu]

question one is linearly dependent since the determinant is 0

[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.

[christianvelasco]

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!

[dabeeramir]

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

[sanashamsi]

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 !!

[wesselbeer]

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

[President_Starscream]

I think I sprained my brain trying to keep up.

[loveyourself]

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 😊

[bao]

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