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Linear Algebra Example Problems - Spanning Vectors #1

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Course website: www.adampanagos.org/ala
In this problem we work with the vectors v1 and v2 and determine if the set {v1, v2} spans R2.
If the set of vectors {v1,v2} spans R2, then ANY vector from R2 can be written as a linear combination of these vectors. To see if this is true, an arbitrary vector from R2 is selected an and an augmented matrix is constructed and solved.
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!

Опубликовано:

7 мар 2015

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Комментарии : 54

@ducksoop.x 4 года назад

Been staring at my textbook for an hour and this video finally got it through my head. Thanks.

@catarina2289 6 лет назад

Oh! very well explained. At last, I was able to get the problem and was able to solve it. Thank you so much! More videos to come.

@AdamPanagos 6 лет назад

Glad you were able to get it figured out. Best!

@hectorramirez626 6 лет назад

Wow. Always had trouble fully understanding this concept until watching this video, I always wondered what it meant and not until I watched this video did I fully grasp the concept. Very well explained. Thank you!

@AdamPanagos 6 лет назад

Glad I could help, thanks!

@mtb8300 6 лет назад

This video is fantastic, I also love the fact that we don't have to sit around waiting for you to write things, I hate that in other math videos.

@AdamPanagos 6 лет назад

Glad you like the video, thanks!

@parassharma105 5 лет назад

You are a legend for putting so much effort & time into making all these videos. The best thing about you is the format & presentation, whatever tool you are using it's great. It's so clear, precise and you explain so good. THANKS AGAIN SIR!

@Amirak254 3 года назад

u just said it for me

@ashutoshkumarjha41 3 года назад

Simple and glittering way of explaining.

@Clairesuismoimaispas 6 лет назад

Thank you Prof Panagos! This Linear Algebra series is great!! Really helpful! Would you please do more Advanced Algebra videos? I am a Math major student and I got to say watching your videos is so much fun!

@AdamPanagos 6 лет назад

Glad the videos have helped. I'm continuing to make more videos as I have time. Hopefully I'll get to some more abstract algebra concepts at some point in the future. Thanks for watching!

@rajp5307 6 лет назад

Very well explained, sir😊 Pretty easy to understand!

@homayounyaqobi792 4 года назад

Thanks for the useful examples. You made a lot of efforts for these examples. You are a great man.

@AdamPanagos 4 года назад

Glad to have helped; thanks for watching.

@nandanaab387 6 лет назад

Thank you sir for making my concepts perfect

@adeci 3 года назад

Amazing! Thank U ! You saved my life!

@jan-willemreens9010 2 года назад

...This video makes me happy, Adam. Using a not too difficult example, Spanning vectors are clearly explained! Thank you, Jan-W

@AdamPanagos 2 года назад

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, Adam

@jan-willemreens9010 2 года назад

@@AdamPanagos ...Thank you for your kind reply and recommendation, I will definitely do that after watching several Linear Algebra videos of yours, as well as recommending your website and youtube channel to other friends interested in Linear Algebra or possible other topics! It really is a jungle of Mathematics on the internet, hence many thanks to you for providing more manageable structure in this... once again Adam, thank you very much! Jan-W

@RAVIPrakash-oq5ed 5 лет назад

Best video on spanning ..thank you so much for this!

@AdamPanagos 4 года назад

You're very welcome, thanks for watching!

@parasbansal5667 2 года назад

this video is really helpful, just before my exams - thank you

@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

@mariabaloch9713 6 лет назад

Best. Video. . . Explained well

@AdamPanagos 6 лет назад

Thanks!

@user-bu8mg7uq3s 2 года назад

thanks

@TrusfratedMochi 5 лет назад

Thanks sir. Great explanation 👍🏻👍🏻👍🏻

@AdamPanagos 5 лет назад

Glad I could help, thanks for watching. Make sure to check out my website adampanagos.org where I have a lot of other videos and resources available that you might find helpful. Thanks, Adam.

@kenethoboyi3343 2 года назад

It is clearly explained and I was able to understand span of a vector

@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

@dailyscienceexperimentsand2761 Год назад

Nice explanation 😀

@AdamPanagos Год назад

Thank you for the kind words, I appreciate you watching. Make sure to check out my website adampanagos.org for additional content (600+ videos) you might find helpful. Thanks, Adam

@bloodustmain6434 4 года назад

Thank you!

@AdamPanagos 4 года назад

You're welcome. Glad I could help, thanks for watching.

@xiaoqingtian6542 4 месяца назад

Bes video for the vector span

@DavidMOUSSONGA Год назад

for two vectors to span a space they should be linearly independent , isn't it sir?

@princesschara Год назад

excellent video!

@AdamPanagos Год назад

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, Adam

@princesschara Год назад

@@AdamPanagos i love you

@rayanegaiba8887 3 года назад

Thank U!!

@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.

@d3vilscry666 3 года назад

At 2:50, you said x1 = a times a-b over 3. Did you mean minus?

@AdamPanagos 3 года назад

Yes, sorry for misspeaking. You are correct. "a MINUS the quantity......"

@sinethembasithole3074 2 года назад

Hi Can I ask, how did you compute your a and b

@AdamPanagos 2 года назад

There isn't any computation for a and b. The values a and b are just arbitrary elements of the R2 vector [a; b]. They are variables; they aren't computed. We're seeing if for ANY values of a and b, we can write the given vectors as a linear combination to yield [a; b]. It turns out we can if we use the values of x1 and x2 computed in the video. So, no matter what a and b are, using x1 = a-(a-b)/3 and x2 = (a-b)/3 yields the linear combination x1*[1; 1] and x2*[1; -2] equal to [a; b].

@Becarefulthismath31.4 4 года назад

Hello The video is very beautiful And one question please Why do you this E2=_1/3E2 But you can do this E2=3E1+E2 And continue the solution

@AdamPanagos 4 года назад

Yes, what you suggest is fine as well. There are always MANY ways to do row reduction and still end up at the correct/same answer. What specific steps you perform is often just personal preference (similar to how people might simplify algebraic expressions in different steps but still end up at the same final answer). Hope that help! Adam

@Becarefulthismath31.4 4 года назад

@@AdamPanagos Well done, thank you

@AdamPanagos 4 года назад

@@Becarefulthismath31.4 You're welcome, thanks for watching!

@fahxaidhe7668 5 лет назад

Da best

@AdamPanagos 5 лет назад

Thanks for the kind words! If you found the video useful make sure to check out my website adampanagos.org where I have a lot of other resources available and consider supporting development of new videos through www.patreon.com/agpanagos. Thanks for watching! Adam