Linear Independence
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- Опубликовано: 8 фев 2025
- We need to be able to express vectors in the simplest, most efficient way possible. To do this, we will have to be able to assess whether some vectors are linearly dependent or linearly independent. How can we make sure that vectors are linearly independent?
Script by Howard Whittle
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Sorry everyone, the first checking comprehension should be linearly dependent, that's my fault!
All good man we love you
Sir nice explaination
Thank you sir
Hmm, I thought I did a mistake and checked the answer by finding determinant, and got linear dependent as the answer :) Thanks for the comment.
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the linear independence of the polynomials were the only thing I skipped of this whole playlist.
guess what came on my test today :')
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Just finished the first comprehensive question and it should be linear dep, i tried switching the vectors around in case i got it confused and i still got the det=0
Yeah you r right.
I also found it linearly dependent by both method.
You are right
Same here 🤚
Yeah i also found the same
it might be a typo .
I got the same answer
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question one is linearly dependent since the determinant is 0
Exactly, I was so confused😅
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Professor Dave, please do something to let people know that the first comprehension question should actually be linearly dependant as it really confused me. Thank you so much.
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Isn't the answer to the first comprehensive question linearly dependent? The determinant being 0.
ruclips.net/video/Ca_IDhOR868/видео.html
Linear Independence and dependence of vectors
@@mkacademy3908 hello! how are you?
yes
I'd the same answer... it's linearly dependent
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It make sence 🥹
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Simply & clearly ❤️
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Beautifully explained
Hi professor,
@7:14 we could end up with 2 equations with 3 unknows, as you've stated, however, if we take an extra step --> R1 = R1 + R2
this will lead to:
[[1, 0, 7/2],
[0, 1, 3/2],
[0, 0, 0],
[0, 0, 0]]
It's not clear why you didn't take the extra step.
I tried it out in Python and the output is as above and it shows that column 1 and column 2, vectors, are the only linearly independent columns(vectors).
but above, in solving the system of equations you've not specified which of the vectors are linearly independent . Have I mis-understood the interpretation here?
Thanks in advance.
Elvy
thanks, needed this
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Thank you so much .
super explanation .....
the first question in checking comprehension shouldn't be linearly dependent since the determinant is zero?
Yeah it is linearly dependent, also = + 2.
@@antonholm114 I think so. I made calcultations and the determinant was -5+10-5, so, it means 0. 3 linearly dependent vectors.
@Mostafa AL Fatih lmao
Yes, it is Linearly Dependent. I checked both row reduction and determinant method.
I had also stumbled upon such concepts. You see the thing is a matrix having a trivial solution means that on putting the unknown in the linear eq we should get zero so Ax=0 but in case of a determinent there are no unknown variables an determinent is purely of enteries of a so both have different results Having a non singular determinent means that this matrix has linearly independent coloumns as there is a property that states if any two coloumns of a matrix are identicle in any way then |A| = 0
Comprehension 1 is DEpendent right?
Yeh i think so, i just calculated it two times, it is sure dependent
Interesting explanation, different from the typical explanations in engineering mathematics classes. This video is definitely easier to understand but seems lacking in the number of theorems covered
It would be really nice if you could apply this easy explanations on a wider range of thopics and deeper level, it would help many crash their maths courses completely!
Thank you
8:17 determinant is zero then dependent
THANK YOU!
Can anyone explain how the checking comprehension's second question is Linearly Independent,
After row reducing it into its echelon form im not getting an Identity matrix .
Any help is greatly appretiated !!
This is the matrix you get from combining vectors a, b, c:
[ 1, -1, 2]
[ -3, -1, -2]
[2, 2, -3]
[1, 5, 3]
Done right, row reducing that matrix will eventually give you:
[1, -1, 2]
[0, 1, -1]
[0, 0, 1]
[0, 0, 0]
So, writing that up with scalars and equating to zero, we get:
c_1 - c_2 + 2c_3 = 0
c_2 - c_3 = 0
c_3 = 0
Inserting c_3 into the first 2 equations, you will get:
c_1 = 0
c_2 = 0
c_3 = 0
This makes the vectors linearly independent.
@@Flunkerenthe second one of the vector is [ -3, 2, -2]
So the row operations are completely based on us, and you might get the answer as linearly dependent or independent and is that right? I mean can a set of vectors be both linearly dependent and independent as well , which is just based on the row operations?
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prof please did you finish the calculus series ? thanks in advance
yes i did, on to other topics!
@@ProfessorDaveExplains should i watch it before the modern physics series and what is your advice for me to get better in it ? and again thanks for the great effort Mr Dave
hmm well i didn't include almost any math in my modern physics series so you can definitely watch those right away, i may learn more physics at a later date and do more rigorous tutorials on those subjects at that point.
7:41
i dont get it. This matrix is still going to be linearly independent though its last row is all zeros? And it is independent because we can see that all of the terms (I mean c1, c2, and c3) are equal to zero?
sir in checking comprehension 1st question is linearly dependent
Thank you Sir
1 comprehension checking is linearly dependent.
Thanks king
What is the answer for the 2nd comprehension?
second comprehension is also linearly dependent? Since there are 3 equations and 4 unknowns , even if we get leading 1 in all the rows, there will be one free variable....hence the vectors are linearly dependent....this goes without solving or reducting the matrix. Is my understanding correct?
Kindly respond
thankyou sirr
thankss 😭🙏
does anyone have a solution for the second comperehension exercise? pls help!