Linear Dependence and Independence - Geometrically

Learning Objective:
1) Visualize what it means for a linear combination of vectors to be zero
2) Rewrite a linear combination in terms of one of the vectors (as long as it has a nonzero coefficient)
3) Define linear dependence and independence

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[dhruvupadhyay]

I watched the same concept in hindi but the way of your explanation was just loved it

[abhirajkamal]

So well explained! I am 16 year old Indian kid and I am studying Vector and 3D these days. I have read a lot of books of renowned writers like SL Loney, Hall & Knight to know about geometric meaning of LD Vectors but I couldn't find what I was looking for. I have always wanted to know the geometric meaning of Linearly dependent and independent vectors but no one could explain the geometric meaning of it to me. Yours is the only video on youtube that could finally help me clear my doubts. Thank you so much! I'd like to know if you connect with math lovers on you channel's social media accounts

[sudarshann]

If you were my teacher and taught our this class, I would have stood up and given a big 🙏 to you . ❤️

[pjakobsen]

Excellent explanation of a topic that is hard to explain.

[VRTX_-scdx]

in 8 minutes you helped me understand what I've been trying to wrap my head around for the past few days, thank you so much

[sudarshann]

I'm not able to stop myself taking your classes, we all love you

[leoyu]

Your illustration is the most easy-to-understand one among all videos explaining linearly dependence! Even better than uni's lecture!! Thanks sir!

[milanaryal]

This video gave me clear concept. I was thinking of the combination of all given vectors will end to the same point where it was originated from. We can change the Direction or magnitude by multiplying by positive or negative scalar if required. Got it.

[kelvinthehuman]

Love too from the Dominican Republic...It's greatly appreciated the time you devote to these jewelry of topics.

[spagoevo]

Man I swear thanks for opening my mind. I’m trying for 3 weeks to understand this and now it has become so easy. I hope god or however u like gives you health and success to continue this and help us. Thanks again.

[IAmTheRealUsopperGoddamnit]

Great video! You graphically explained it as well, which is what I was looking for :)

[sepehrkhosravi]

I don't understand the last example. Can i not use x and z to construct y? wouldn't this make it dependent?

[lebalen]

you are great, thanks for these fantastic videos

[j.k.sharma]

Your are very very good explainer. Love from india

[thaidoan]

I love you so so much... Thank you very very much. I have no words to say, you are awsome !