At 9:30 You can easily prove the theorem that if there's more vectors than dimensions in a vector space, than there must be at least one linear dependence by way of the pigeonhole principle. The pigeonhole principle says this same thing but it's more general; that if there's B spaces and greater than or equal to B+1 items, then there must be overlap of more than one item per space.
I was struggling with linear dependent mean no new info was added now it is clear but there is further more thing i need to learn than simple calculation
{TheEmptySet} make an even bigger matrix B. Then rewrite matrix 1 as first column in B, matrix 2 written in second column of B, etc. Solve for the homogeneous matrix B, like he does in the video.
For any future viewers thinking the same .. you can divide the bottom row by 13 (13/13) to get 1 since the answer (0) will not be affected --> full rank --> linearly independent
@@jacobm7026 Yeah I don't get it because surely one vector can be a linear combination of another so it would be redundant making it linearly dependant or am I missing something? [edit] never mind he answers it in 14:00
3 years late, but when you completely row reduce to reduced echelon form, u find that the last column is (0 0 1). Which is a pivot column. What he did was he used the 13 as a leading entry in echelon form, which also signifies that it is a pivot. Both ways work, but I find the reduced echelon form where the last column is (0 0 1) a bit easier to understand.
When the solution is trivial, the vectors are linearly Independent then how comes in the last 1x1 zero matrix, was your solution non-trivial! You just declared it Dependent, cah like bruv wtf
![[Linear Algebra] Linear Transformations](http://i.ytimg.com/vi/cFIRXQBfgg0/mqdefault.jpg)
![[Linear Algebra] Linear Transformations](/img/tr.png)
![[Linear Algebra] Span of Vectors](http://i.ytimg.com/vi/t_59feLJVIQ/mqdefault.jpg)
![[Linear Algebra] Homogeneous Linear Systems and Parametric Form](/img/n.gif)
At 9:30 You can easily prove the theorem that if there's more vectors than dimensions in a vector space, than there must be at least one linear dependence by way of the pigeonhole principle. The pigeonhole principle says this same thing but it's more general; that if there's B spaces and greater than or equal to B+1 items, then there must be overlap of more than one item per space.
Best video series of Linear Algebra that i have seen
i dont know why it has got so less views. it is one of the best lecture.
True
True
True
True
Thank you! This video really helped explained things far more clearly than my professor ever did.
By far the best linear algebra professor. THANK YOUU
just want to say thanks watching these videos while learning from sheldon axler linear algebra textbook and it really helps. thank you
Thank you so much! This is the first time I'm really able to visualize this concept
These match with my uni course sequence perfectly, thank you so much
maths 235 perhaps?
This is good ...thank you so much .... I am now going to look at all of your work (most of it .... this sentence is linearly independent)
Thank you! I was struggling with this concept and now it makes perfect sense!
Big thanks for the videos! Easy, clear explanations . Keep up the good work, champ!
This is extremely helpful. Thank you.
6:11 what if i have something like 2x1 = -x2, is it dependent then?
Thank you for the video! Helped me understand
you are the best trev
Hey, great video but I've one question. Why did you multiply all the vectors by 0 (min 14:40)?
thanks so much your videos are so helpful
Thank you so much. You are such life saver
whoa that name
I don’t usually comment but thank you for making these videos
if a set of 3 vectors are linearly dependent, would the vectors span r2? would the set of m vectors have to be linearly independent to span rm?
I was struggling with linear dependent mean no new info was added now it is clear but there is further more thing i need to learn than simple calculation
Which book he used to explain these questions Kindly tell the name of book . Thanks in advance 😊
@TheTrevTutor How do I determine, if matrices are lineraly dependent?
{TheEmptySet} make an even bigger matrix B. Then rewrite matrix 1 as first column in B, matrix 2 written in second column of B, etc. Solve for the homogeneous matrix B, like he does in the video.
You are the great,,,, love u
I think the example you used is linearly dependent cause of 13
For any future viewers thinking the same .. you can divide the bottom row by 13 (13/13) to get 1 since the answer (0) will not be affected --> full rank --> linearly independent
what if the no of equations and unknowns equal?? still we have to solve and check right?? we cannot conclude anything without solving? am i right??
correct
@@jacobm7026 Yeah I don't get it because surely one vector can be a linear combination of another so it would be redundant making it linearly dependant or am I missing something? [edit] never mind he answers it in 14:00
god fucking bless you man
I wish more professor would explain geometrically what happens when we do linear so we could actually under stand wtf is happening.
Im a little confused how there are no free variable when not all the columns have a 1. The last column has (-1,4,13) how is this not a free variable?
3 years late, but when you completely row reduce to reduced echelon form, u find that the last column is (0 0 1). Which is a pivot column. What he did was he used the 13 as a leading entry in echelon form, which also signifies that it is a pivot. Both ways work, but I find the reduced echelon form where the last column is (0 0 1) a bit easier to understand.
I really don't know how he got the row 0 -2 5 at 4:55
he took the second row and multiplied it by -5 and then added the third row to give the new third row : -5R2 +R3 --->R3. where R = row number
@@drakeahmed5133 thank you very much sir!
Guys did anyone understand the theorem and the proof?
When the solution is trivial, the vectors are linearly Independent then how comes in the last 1x1 zero matrix, was your solution non-trivial! You just declared it Dependent, cah like bruv wtf
no dislike yet. rare
Plz make hindi or marathi