More on linear independence | Vectors and spaces | Linear Algebra | Khan Academy

More examples determining linear dependence or independence.

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[samdavepollard]

This guy could walk into any university and explain stuff better than at least 90% of professors on staff.
Many Thanks.

[Chashi]

Sir you are really Brilliant... excellent lecturing skills... I wish you were at my University... Keep up the good work.

[RegretForNothing]

thank you...ive been passing exams like a mad man thanks to you.

[guerillachan]

Oh man your amazing you saved my life I got exam soon and our teacher goes so fast its hard to understand him you break down so well your heaven sent.

[nirajkc]

I never got the concept so clear as this before. Many many thanks.

[lfi]

I watch this in class instead of listening to the professor

[ryuusel]

You're absolutely right. I was initially confused because I thought of an example where his definition didn't work. For example, if a=1i, b=-1i, c=1j. These three vectors are clearly independent. Also, 1a+1b+0c = 0. By the definition he gave, these vectors should be dependent. Thus, his definition doesn't work as stated. After I saw him work some problems, I realized that his definition was intended for vectors with the same number and type of components. I posted a correction stating that.

[maksimreshetnikov]

"...dealing with linearly dependent network... oh... linearly dependent set..."))) this guy, for sure, knows more than he is speaking to us)))

[TheDarkLobster]

can't believe this is all on youtube, thanks so much

[tovelundberg]

So much better than both my lecturer and book. Love it!

[frostpistol]

I love this video, u r much more better than my 2 teachers, i couldnt  undrestánd these in 3 lection but i undrestand perfectly in 17min here, thanks alot

[tongclairexu]

The first example (6:55)is a system of 2 equations with 2 unknowns, therefore there is one set of answers only, (0.0)
The second example(11:16), however, is a system of 2 equations with 3 unknowns, the answer of c1=0, c2=0, c3=0 satisfy the equation as well. The rule like Sal said is that if all Cs are 0, then the system is independent. But the second example is concluded as linearly dependent. How do we then go about determining independence and dependence? I maybe missing something here; if anyone can clarify, or add to any holes in knowledge I may have, thank you!

[bangvu]

Thanks for great explanation! Was struggling to understand why it must equal to zero.

[shuainero]

Thank you for adding other languages subtitle

[fatboyj]

My thanks spans R^n with linearly independent vectors because my grades on my quiz were all members of zero

[skyly]

These videos make me thirsty for knowledge like never before. Thank you so much

[novinnouri]

thanks for explain.thats nice example....this video better than previous video

[tracysara]

I was 8 years when this was uploaded am watching it at 20 yrs you for sharing your knowledge

[pravinmhaske]

Amazing. These along with the 3Blue1Brown videos on Linear Algebra and you don't need any books to understand vectors and LA.

[clairebeanbagchair]

This is amazing. I am doing this just now and i have a textbook that i paid £50 for, and i still couldn't understand what it means! Thank you so much. Keep making videos, i will probably be back here as my course gets harder :P