Span and Linear Independence Example

[nowjustthinkaboutit]

wow. thanks so much! Hugs and kisses

[Savl0r0]

Thank you soo much , it really helps

[hjhhkq]

can someone please tell me which program he is using?

[ja2smart92]

I always like to imagine that its Obama teaching me this b/c he kinda sounds like him, especially when he says 'independent'

[mfh69]

better than any teacher at my uni

:-)



[Cracklin319]

Great video, It helps me a lot!

[PhilChern]

what's the program that he uses for the video? im kind of sick of using paint for this kind of stuff

[GeekBoy03]

@PhilChern it's not a "program". He is using a "pen tablet"

[rocco133]

@PhilChern

i think you mean smoothdraw3.

[HabbaDj]

You should really have used Matrices in this video... Damn that was a lot of C's :P

[DrunkinHulk]

better than my teacher butr still got lost towards the end.

[ste8ven]

you missed adding a b to C3

[yoman437]

you are more than awesome.. love al your video...

good job man, n thanks a lot.....

[omgthatscrazyx]

Sal , I want to shake your hand

[dauntSilver]

Just what I was looking for.. only I use matrices instead of adding/subtracting the equations as shown.

[TheLiberalSoup]

man, great explanation.

So many 3s, cs etc. I was about to say in my head "plus c-3po"

[adrian549092]

Great video very lear you've helped me out completely, keep up the good videos...

[niiidar]

Why is he reducing the matrix in this way? Seems tedious...

[fireproofazn]

thank you for saving me from killing myself. please never stop making these tutorials.

[roachey15]

Anyone else notice the fart at 3:53? lol..probably need headphones to hear it. Great video though.

[tautologicalnickname]

great great video!! very helpful!

[ironlobsta]

thank the lord for youtube

[andreispyes007]

Yesterday , i had no ideea on linear algebra, but watching this videos has enlightened me .

Thank you Sal.

[DreamShot92]

This will definately help me with my final is 3 days!!! Thank you!!!

[LAnonHubbard]

Very watchable. It's amazing how much ground you're covering as I've tried to learn this from text books before and didn't get as far. Mind you, trying to learn it from other sources will have helped me too I think.

[yongro8912]

better than my prof.

[ksb916]

This video makes it so clear, thx

[1LastMeal]

you the best that's all i can say.

[nazhy00]

A reduced row echelon form matrix would've done the solution fast

[demonicsin11]

this is very helpful! thank you so much!

[PeterCornstalk]

This made me sleepy and hungry. 

[hkpopfan4lif3]

You confused me at the end when you said that system is linearly INdependent.

It WOULD be if the vectors equal the 0 vector, but you only used the 0 vector as an example.

What if they equal something nonzero? Would it then be linearly dependent?

Meaning, I set a b and c to be 2 6 and 13, respctively. You would find c1 c2 and c3 to be something other than zero, right? That would be dependent?

[Taowhr]

Oh I get it now, this whole thing is just systems of equations!

[colverj]

When working out if it spanned R3, what problem would have occurred if it did not span R3? i.e. would you use the same method if the question asked to prove if a set of vectors did not span the vector space

Thanks

[Raidel007]

Thanks for the help.... I finally found a good explanation

[maong78]

ahhh linear algebra final tmr!! D:

[LoadofSlap]

"Linearly independent if the only solution is 0"

How do you know the only solution is 0? You've only shown that one of the solutions is 0 surely?

[dtomasiewicz]

@LoadofSlap If there were multiple solutions to the system of equations, there would've been a variable (a parameter) in the "final" values for c1, c2, and c3. There was no parameter (they all came out to be 0), and so the system only had 1 solution, the trivial solution (all zeroes), and so it is linearly independent.

[LoadofSlap]

@dtomasiewicz Thank you, this makes more sense to me now.

[WildChildftw]

Wouldn't it be easier to show that the set of vectors are linearly independent. If they are, they are guaranteed to have a solution or Ax=b, where b is an nx1-matrice.

[kapification]

Holy shit!

wonderful video

Thank you so much!!!

[JashanSKang]

thank you so so so much for doing this now everything is clear

[yynotx]

great job--i missed the role or scalar constants in defining linear independence when i read this in a textbook--its really communicated well in these 3 vids...

[MsEwander]

He made a mistake with C3, it should be 1/11(3c-5a+b), he forgot about b - that's why the whole answer is not correct. But very interesting interpretation - I like it :)

[HandOfCode]

Correct, he missed one calculation.

He still got the answer right that they're linearly independent. (using row-reduction you get the identity matrix)

[George8L]

@MsEwander if you watched all of it you would have seen that he corrected that mistake...

[vvviiikkkaaa17]

Maybe I don't understand this correctly but your answer seem to be wrong. Let's say i have a vector V=(1 2 3)' (i.e. a=1, b=2 and c=3). Then according to your solution, c_3=6/11, c_2=13/11 and

c_1=-21/11. But when you put the solutions into the equation, the equation on the left side doesn't equal the one on the right side. Am i doing something wrong? please help me figure it out

[vinso334]

Thanksssss so Much it helped alot i have a linear test tomorrow and i totally understand!!!

[itzmattu]

Thanks for these videos! It's a huge help in trying to prepare for my exam this morning. What program do you use to do the math in these examples?

[prakashltpm]

Excellent Video. You created a new interest in learning maths within me.

[joeyjoey1122]

eigenvectors would be interesting.

[myselfable1]

great series.

Will you do a show on the Eigen value problem

and then the link it to differential equations?