Span

[@drpeyam]

At the end it’s 2h+7, not 2h-7, so the correct answer is h = -7/2

[@lambdamax]

Thank you for your consistency. My knowledge spans multidimensional degrees now. I shall tackle higher order systems in life from now on. Hopefully, life is non-trivial.

[@mazenelgabalawy3966]

how is this comment made three days ago if the video is two hours old??

[@Zonnymaka]

You spoiled the fun! LOL

[@mazenelgabalawy3966]

@@GhostyOcean OK thanks for the info

[@shoopinc]

OH, that makes sense

[@drewpat9535]

Dr Peyam, your enthusiasm is One of the key of the success of your beautiful Channel! Don't even spill a drop off!!!!

[@s0areslucas]

Dr. Peyam is the best mathematician on KZbin!

[@JO-ej3nh]

You explained it way better than my professor did. Thank you!

[@secretsquirrel4375]

I love this!! I’m in linear algebra right now and we just finished covering span today in lecture. Recommending you to the rest of my class. Great job!

[@drpeyam]

Thank you!!!!

[@rogerkearns8094]

I found this in my span folder.

[@drpeyam]

Hahahaha

[@koenth2359]

Unfold it to its full spanwidth!

[@raminrasouli191]

Thank you very much for explaining both graphically and verbally this problem. I was looking for such clarification in a long time.

[@juandeluna2652]

Thanks for your tutorials dear Dr Peyam.

[@adamhrankowski1298]

This particular example is simple enough to do mentally, because of the zero. b has to be -5: -5*0 + -5*1 = -5. Then, -5*8 = -40. --3-(-40) = 37. (37/-2) * -2 = 37. Therefore a = -37/2. (--37/2)*1+ (-5)(-3)= -7/2 = h. And that's it.

[@koenth2359]

This case is easy (h,-5,-3)=a(1,0,-2)+b(-3,1,8) It folllows immediately that b has to be -5 and hence that -3=-2a+8b=-2a-40 so that a has to be -37/2 Then h=a-3b=-37/2+15=-7/2. Glad however that you showed the generic method for less straightforward examples!

[@technogamerz2033]

THANK YOU SM DR PEYMAM

[@MrAkindos]

It's enough to form a determinant with these three vectors (h;-5;-3), (1;0;2), (-3;1;8) and set it to zero as these three vectors are linearly dependant.

[@drpeyam]

Ok, but then what is a span? 😉

[@happyfrogkhmel]

Your videos are wonderful

[@mehdisi9194]

Thank you dr peyam I also think you could calculate the determinant of the matrix whose columns consist of these three vectors and got it equal to zero and then you could get the value of h

[@jeremyb1346]

Another approach could be: For which h, is (h,-5,-3),(1,0,-2),(-3,1,8) not a basis? For which h is det((h,-5,-3),(1,0,-2),(-3,1,8)) = 0 ? det((h,-5,-3),(1,0,-2),(-3,1,8)) is the determinant of the matrix composed of these vectors that you can easily calculate with the "bomberman" method (see dr peyam's video) nice video btw

[@drpeyam]

Yes, but that only works for n x n matrices, and doesn’t explain what a span is

[@jeremyb1346]

​@@drpeyam Yes, obviously if someone asks "why?" we need to go back to the definition with linear combinations, span, etc.

[@egillandersson1780]

I think there is a sign error : the bottom right value in the last table must be 2h+7. So 2h+7=0 => h=-7/2. Isn't it ?

[@drpeyam]

Correct

[@vanessakitty8867]

Your zipper hoodie looks very nice. TY for the Linear Alg. lessons.

[@drpeyam]

Thank you!!! Blackpenredpen gave it to me!

[@carlo6382]

Is the overdetermined system (overdetermined cuz equations>variables)unique or infinite solutions??

[@aakabeer7901]

I Love linear algebra

[@drpeyam]

Me too!

[@nootums]

Hey Dr.Peyam! I love your videos!!! I had a question- while doing indefinite integration, why do we get different answers based on the method of solving? Generally a -ve sign pops up in one of the methods. Thanks!

[@drpeyam]

They all differ by a constant. All indefinite integrals are the same except for a constant

[@opufy]

Thanks, doc!

[@TheMauror22]

Will you do a video about geometric and algebraic multiplicity of eigenvalues? Please do it! That would be great!

[@drpeyam]

Will do later

[@harikishan5690]

wow this is so useful,first i was thinking of taking a.(bXc)=0,since they are in the same plane and solving for h,but this is just way easier,without all that multiplication😂

[@drpeyam]

Not only that, the cross product only works in 3 dimensions, this works in all dimensions!

[@sirshaganguly7706]

I love your smile ;)

[@garrytalaroc]

Legendre Equation

[@Tomaplen]

Wake me up... when your linear algebra course ends... (8)

[@drpeyam]

Might take until September 😂

[@Tomaplen]

@@drpeyam HAHAHAH damn :(

[@chucksucks8640]

I have an approach that is way easier for this problem. We know that this is a consistent system and that b = -5 by the second row. Substitute that into the row 3 equation and get a value for a which would be -37/2. Now substitute both of those values into the first row and get the correct answer of h = -7/2