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Linear Algebra Example Problems - Linearly Independent Vectors #1

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Given a set of vectors we want to determine if they are linearly independent or not (i.e. linear dependent). A set of vectors is linearly independent when the linear combination of the vectors is equal to an all-zero vector only in the trivial case when all combining coefficients are zero.
Thus, to determine if a set of vectors is linearly independent, we just have to construct and solve a homogeneous system of equations. If the only solution is the trivial solution, the vectors are linearly independent. If there are more solutions than just the trivial solution, the vectors are linearly dependent.
If you enjoyed my videos please "Like", "Subscribe", and visit adampanagos.org to setup your member account to get access to downloadable slides, Matlab code, an exam archive with solutions, and exclusive members-only videos. Thanks for watching!

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18 мар 2015

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Комментарии : 81

@halilsmith8162 9 дней назад

These explanations are a million times better than my professor. Thank you so much!

@putinscat1208 3 года назад

This is great. You expressed this in math instead of guessing, voodoo, or other explanations from teachers that are confusing.

@user-km6kg3nn5x 6 месяцев назад

lets assume

@The2AmInventor 7 месяцев назад

someone who is clear and concise, just added your lin alg playlist to my "Best Math Videos I have ever watched" playlist.

@web_walkerX 7 лет назад

thanks man, this video saved me from losing ten marks

@sanpreetkaur3071 6 лет назад

I have a midterm in 20 minutes this just clear all my doubts! Thanks a lot! ❤

@AdamPanagos 6 лет назад

Glad I could help; hope the midterm went well!

@willlowry5170 5 лет назад

short and right to the point. Thanks so much!

@travisbodhaine7837 5 лет назад

Before I even watch the video I make sure to Thumbs up it! Thanks for being such a great teacher!

@AdamPanagos 5 лет назад

You’re welcome, thanks for watching. If you found the video useful make sure to check out my website adampanagos.org where I have a variety of other resources available that you might find helpful. Thanks, Adam.

@muhammadkumayl7761 7 лет назад

The real OG. Good stuff man

@Libertycity56 3 года назад

I have the world's worst math professor who not only sucks at teaching, but the textbook is literally his notes written at a PhD level so my only option is to self-study. Thank you for breaking this down!

@AdamPanagos 3 года назад

Glad I could help, thanks for watching. Make sure to check out my website adampanagos.org for additional content (600+ videos) you might find helpful. Thanks, Adam

@Amoeba_Podre Год назад

im in the same boat. The worst part is that he has an accent that makes it difficult to understand him at times

@serinacat4781 7 лет назад

oh my god, I am in math major. you mind is very clear. your linear algebra vedio is better than khan and mit. you saved my life👍👍👍👍👍😃😃😃😃😃

@gaddiji 17 дней назад

how to do this, augmented matrix and row reduction thing?

@baueranthony54 2 года назад

This is great and really helpful! The spanning videos really help to. To go one step further for my understanding, if I wanted to determine if these three vectors form a basis for R3, all we'd need to find if they span all of R3?

@AdamPanagos 2 года назад

Yes, that's correct. A basis for R3 is just a collection of vectors that can be used to write any element from R3 (i.e. they span R3).

@ngocly8844 8 лет назад

Thanks for make me more understand it

@sgifford1000 4 года назад

Nice quick explanation with examples! Thanks!

@AdamPanagos 4 года назад

You're welcome, thanks for watching!

@Faiisan 8 лет назад

Great video thanks!!

@Adam-gp3ij 5 лет назад

Thank you professor! That was really clear

@AdamPanagos 4 года назад

You're welcome, glad I could help.

@gopakumark1576 2 года назад

Thanks a lot Professor. This has been of great great help.

@AdamPanagos 2 года назад

Glad I could help, thanks for watching. Make sure to check out my website adampanagos.org for additional content (600+ videos) you might find helpful. Thanks, Adam

@FatmaYousuf 5 лет назад

YOU'RE A LIFE SAVER! THANK YOU!

@AdamPanagos 5 лет назад

Glad I could help, thanks for watching! Adam

@fahimimtiaz2153 2 года назад

Bro, you saved my ass during online exam. Thankyou so much

@AdamPanagos 2 года назад

Glad I could help, thanks for watching. Make sure to check out my website adampanagos.org for additional content (600+ videos) you might find helpful. Thanks, Adam

@capocianni1043 7 лет назад

thank you man ! you are the real man :D

@AdamPanagos 7 лет назад

Thank you!

@mdkalimullah4207 5 лет назад

Thanks sir now it is clear

@codingwithelhacen990 4 года назад

Thank you 🙏

@nuwanatthanayake 3 года назад

Great Work again. Sir...

@AdamPanagos 3 года назад

Thanks for the kind words, I’m glad you enjoyed the video! Make sure to check out my website adampanagos.org for additional content (600+ videos) you might find helpful. Thanks much, Adam

@toheedh 9 месяцев назад

what if its a 4x4 ? is it the same case as in video

@TokitaShell 4 года назад

very useful

@matinhewing1 8 лет назад

Great video! Thank-you!

@AdamPanagos 8 лет назад

You're welcome, thanks!

@user-bu8mg7uq3s 2 года назад

thank you

@sayanbaidya9724 Месяц назад

can prove just by seeing det not equal to 0 ?

@NataleTabb 2 года назад

How would I find a possible solution if my answer is dependent?

@kushagrasonkar 5 лет назад

Hi. Awesome tutorial. Can you please link the row reduction video here or in the description please?

@AdamPanagos 5 лет назад

Yes, here are a few row-reduction videos from the playlist: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-YCyItKPDcSo.html ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-FeGVpk96UqY.html ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-VkYmaBhikYY.html The full 65+ video playlist is here: ru-vid.com/group/PLdciPPorsHuk3Hp7QPPAtTkpW0o1UXQB6 Thanks for watching! Adam

@andrewstructo641 2 года назад

Explains better than Mark solomonovich :P

@mohammadhaidar7319 4 года назад

you absolute legend!

@AdamPanagos 4 года назад

Thanks for the kind words, I’m glad you enjoyed the video! Make sure to check out my website adampanagos.org for additional content (395+ videos) you might find helpful. Thanks much, Adam

@manudas450 5 лет назад

am not understand after r. r? how to write 1000,0100,0010,0000pls tel me.

@phdcsc3383 3 года назад

Thank you!

@AdamPanagos 3 года назад

You're very welcome, thanks for watching. Make sure to check out my website adampanagos.org for additional content (600+ videos) you might find helpful. Thanks, Adam.

@sankoktas420 2 года назад

Legend

@4wtar3 7 лет назад

شكرا لك 👍🏻

@AdamPanagos 7 лет назад

You're welcome!

@BoredChinese 7 лет назад

I don't quite get the 2nd example. Why is X1 = -X3 and X2 = -X3? Did I miss something? :O

@AdamPanagos 7 лет назад

After doing the row reduction, look at the rows of the matrix. For example, the 2nd row of [0 1 1 0] means that 0*x1 + 1*x2 + 1*x3 = 0. So, x2+x3 = 0 which means that x2 = -x3. Similarly, the first row of [1 0 1 0] means that 1*x1 + 0*x2 + 1*x3 = 0. So, x1+x3 = 0 or x1 = -x3. Hope that helps, Adam

@BoredChinese 7 лет назад

Oh I get it now. Thank you!

@BoredChinese 7 лет назад

Btw, do you have a video about the topic row space, column space, and rank? with nullity. I'm not quite sure what it was but that was all I could remember

@AdamPanagos 7 лет назад

Yes, just look later in the same playlist as this video. Here's the first one: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-oefqNuzifsU.html

@BoredChinese 7 лет назад

You're a life saver man thanks a bunch T_T

@yifancheung7842 2 года назад

@AdamPanagos 2 года назад

You're very welcome, thanks for watching. Make sure to check out my website adampanagos.org for additional content (600+ videos) you might find helpful. Thanks, Adam.

@user-vd3bl5ws2e 3 года назад

Tomorrow is my final exam and i Just get it😆 Thanks alot🙏😩

@AdamPanagos 3 года назад

Glad I could help, thanks for watching. I hope your exam went well! Make sure to check out my website adampanagos.org for additional content (600+ videos) you might find helpful. Thanks, Adam

@lingeshwaranramamoorthy626 5 лет назад

Ok when You mention trivial solution do you mean X1,X2,X3 must take same value such as 1,1,1 2,2,2 or they must only take 0,0,0

@AdamPanagos 5 лет назад

By trivial solution I mean the "all zero solution", i.e a1 = a2 = a3 = 0. Hope that helps, Adam

@lingeshwaranramamoorthy626 5 лет назад

@@AdamPanagos thanks

@eylmaz6696 3 года назад

can we use determinat here to say this is linearly independence

@AdamPanagos 3 года назад

Yes, you can. There are lots of ways to show independence/dependence. Using the determinant is fine.

@eylmaz6696 3 года назад

@@AdamPanagos thanks sir, could you put videos related to theorical part ? some of exams are True and false. And also polynomial basis are the another topic that i dont find a source. if you help thans . googl luck sir

@AdamPanagos 3 года назад

@@eylmaz6696 Yes, most of my linear algebra problems are very "numerical" at the moment. I'd love to get a collection of videos created that focus on the more theoretical/proof-based aspects of linear algebra. It's on my list to do, hopefully I'll get to it some day! Thanks for watching, Adam

@ZedWONG 5 лет назад

Thanks for saving my life. Lol!

@AdamPanagos 5 лет назад

Glad I could help, thanks for watching!

@sonniethuynh 8 лет назад

how can you tell without row reduction.

@AdamPanagos 8 лет назад

+Sonnie Huynh It really boils down to figuring out if there's a way to see if any of the vectors are linear combinations of the other vectors. Sometimes one can "just see" that this is true. For example, if two of the vectors are [1; 2] and [3; 6] it's pretty easy to see that [3; 6] = 3*[1; 2] and thus these vectors are linearly dependent (and thus not independent) However, as the number of vectors increases and the dimensions of the vectors increase, one is often not able to "just see" this type of relationship. In this case, setting up the system of equations and solving is the way to find out. Solving the system is often done via row reduction, but you could also use determinant computations and Cramer's Rule to solve. I have another video on the playlist that shows some examples of Cramer's Rule that you could check out if desired. Thanks for watching. Adam