Linear Independence
ฝัง
- เผยแพร่เมื่อ 15 เม.ย. 2019
- 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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Watching this 3 days before my midterm. Man, you saved my life
I'm a sophomore in college. I'm learning linear algebra this time, and it was hard because the professor's lecture at my school was too difficult. I found your channel while I was looking for a supplement, and it was very helpful. Thank you for this. I hope you will continue to make good videos.
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Once again, Professor Dave pulls through with the best, clearest, and shortest video on the topic.
I'm just learning this, but I'm pretty damn positive the answer to the 1st checking comprehension question is linearly dependent. If this was a sly trick to get me to go over determinants and linear dependence, well done Prof Dave.
Yeah, that's my bad. You're right.
@@ProfessorDaveExplains It legit made me understand it more, because I really questioned myself and went over the material again. You're the best. Thank you!
Thank you for this comment. I was scratching my head and wondering if I had misunderstood something, lol.
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question one is linearly dependent since the determinant is 0
You are a very bright and phenomenal teacher. Thank you so much.
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
What a great explanations... Thanks a lot Professor Dave!!!
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very well explained video. I'm sick and have a quiz in 2 hours and I was able to clearly understand everything
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Thanks Mr DAVE keep going
Such a simple explanation thank you so much!
Lovely video, helped me a lot in my Grade 11 exams.
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
The formal definition in our uni sucks. The lecturer sucks also too. I went on to work on my degree using the knowledge from this video and it helped me a ton.
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I think the rip, but we still don't know what dark energy is so that could very well change.
the linear independence of the polynomials were the only thing I skipped of this whole playlist.
guess what came on my test today :')
always watch the whole Professor Dave Explains video kids
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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.
Beautifully explained
Isn't the answer to the first comprehensive question linearly dependent? The determinant being 0.
th-cam.com/video/Ca_IDhOR868/w-d-xo.html
Linear Independence and dependence of vectors
@@mkacademy3908 hello! how are you?
yes
I think I sprained my brain trying to keep up.
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Simply & clearly ❤️
thank you sir you taught in 15 minutes what my professor did in 4 hours
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awesome presentation I actually got the point home
sir in checking comprehension 1st question is linearly dependent
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.
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In the 2nd comprehension question should the vector be written in vertical or horizontal positions to solve elementary row operations?
I mean 4*3 matrix or 3*4 matrix to start solving?
I wrote them vertically. First time I did it I got linearly independent, second time I tried again after going to this video: th-cam.com/video/SOzO9EcQdQc/w-d-xo.html
I got linearly independent the second time around, but it took 11 rounds of elementary row operations.
Thanks
Thank you Dave. This helps me a lot 😊
Best lecture thank you!!!
thanks, needed this
Professor Dave, the first homework question's answer is zero when solved using determinant method, then it should be Dependent and NOT Independent
Thank you so much!
how does one solve the 2nd problem in 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
YOU ARE A LIVE SAVER, i've being reading my text book for like a week trying to understand vector space and this stuff but just watching your videos taught me so much, thank you so much dude
Thanks!
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?
thank you professor dave
How did the first illustration change from a+2b to 2a+b I thought b was the one with the coefficient of 2 and not a
Thanks sir!!!
Thank you so much .
Great Video!!
Simplicity is the most elegant form of complexity
Unsure if you still check comments on these videos, but in the example where you added 3 length 4 vectors together could you also add another length 4 vector with the value (0,0,0,0) in order to construct a square matrix then find its determinant to see if the 3 vectors are linearly independent?
hi, i don't think so. a matrix with a column of zeros will always have a determinant equal to zero, but it is possible to have 3 linearly independent vectors (even though they are all of length 4). whenever you don't have a square matrix, you'll have to solve it through elementary row operations. :')
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and I am in Grad school now still watching his videos.
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sir can you try the second comprehension question once again
Comprehension 1 is DEpendent right?
Yeh i think so, i just calculated it two times, it is sure dependent
thank yu sooooo much teacher
great job
Thank you
What if one of the variables in the matrix does not have a value. For example, you are trying to find which of the following vectors are linearly independent: c1 (1, a, 0) + c2 (a, 0, 1) + c3 (0, 1, a)
You simply put it as a 0 in the matrix and solve
What is the answer for the 2nd comprehension?
love your videos
in the test your comprehension by determinant method, determinant is zero so its linearly dependent but video says otherwise..can someone explain?
where we use the linear independence?
Hi there, would it be possible to have a solution for the second comprehension question. I worked through the question 3 times and every time I get linearly dependent.
Ok I tried it again and got linearly independent.
@@CHEESYhairyGASH how?? I tried to solve it in multiple ways and always get linearly dependent, i always end up with 3 equations but 4 unknowns -> free variable -> linearly dependent
Plz answer as fast as possible as i have an exam tomorrow 😅
does anyone have a solution for the second comperehension exercise? pls help!
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.
Best video
Hi Prof.
Please I think the exercise you gave at the end of the video is supposed to be be linearly dependent for the eg. 1
yeah, its linearly dependent, see the pinned comment on this video
What if lets say c1= any number other than 0, like 1. If c1=1, it is independent of any other cs, but it is not 0. Does this mean it is independent?
Does the row of echelon have to be equal to one or equal to the top left number? please help!
it doesn't have to be, but it generally makes the other elementary row operations easier to do by hand.
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
Hello professor
Could you pls explain the row by row equations for the second question?
do you know the elemtary row operations for a matrix? if not i suggest youtubing "Converting a matrix to REF form" - youll get it then!
You should check out prof. Dave's linear algebra playlist, he's got a video called something along the lines of "Gauss Jordan elimination"
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