❖ Linear Independence and Linear Dependence, Ex 1 ❖
ฝัง
- เผยแพร่เมื่อ 3 ต.ค. 2024
- 📚 Linear Independence and Dependence Explained - Step-by-Step Example 📚
In this video, I explore the concept of linear independence and dependence in vector spaces, demonstrating what it means for a set of vectors to be linearly independent or dependent. We'll work through a detailed example showing that a specific set of vectors is linearly dependent by row reducing a matrix composed of these vectors.
🚀 What’s covered:
Understanding the definitions of linear independence and linear dependence.
How to determine if a set of vectors is linearly dependent using row reduction.
Step-by-step walkthrough of an example to solidify your understanding.
Tips for recognizing linearly dependent sets in vector spaces.
Whether you're studying linear algebra or preparing for exams, this video will help you grasp these fundamental concepts essential for advanced mathematics, physics, and engineering courses.
👍 Don’t forget to like, subscribe, and hit the notification bell for more math tutorials and insights! 🔔✨
Hashtags:
#LinearIndependence #LinearDependence #LinearAlgebra #VectorSpaces #MathTutorial #RowReduction #Mathematics #MathHelp #STEM #LearningMath #MatrixAlgebra #EducationalContent
How to ace all first year math courses:
1- Go to class, try to learn the basics
2- Watch a Khan academy video to "gain some intuition" for subject
3- Watch every relevant Patrick JMT video to practice solving problems
4- Repeat throughout semester
Brilliant. I did this a few years ago, I still can solve matrices. Just came back to refresh
Oh my God, thanks! This is helpful lol, we can add 3blue1brown to the list of sources to gain intuition
Hi, hope you see this question after so many years...I just started my first semester and during the classes I don't seem to understand literally anything that the Prof teaches, I need to go home an study through TH-cam videos to at least to get a sense of what I'm doing.....is it normal to be like this as a first year student?
@@yakuzzi35 only if you see this as a hobby, for most people watching this isnt, they just want to get it over with
Even if a donkey does all that he will get all A, you think people work overtime? lol man
You have been my prof for at least 3 classes in uni
this nigga has taught me calculus, lin algebra, stats, i owe this guy my degree
Patrick is white!
he's a honorary niggga
M'ShadowCC He is my nigga
Shawn sorry I did get it
Is it linear algebra as in lin algebra or lie algebra (lin as in typo)
My real math instructor
islespatrick Amen.
Preach it
I think that is so because "youtube teachers" are eager to share and teach what they know for no guaranteed return i.e salary. But a lot of "professional teacher" out there are more concerned with their titles and paychecks! Did my first your of Civil heavily backed up by guys like Patrick! If I don't get it there I will surely get it here!
Agreeing on that.
Many distance study institutions could make videos like PatrickJMT & make our lives much easier...
But, I would come back to Patrick a thousand times over, because he "uncomplicates" Maths & makes it FÜN to learn......
Even makes one look forward to the "next lesson" 😉
@@daniloorbolato do you remember which were some of the most helpful channels for civil
To save time if you're asked to determine whether or not the vectors are linearly dependent,
Take the determinant, if its = 0 it is linearly dependent if not it is linearly independent.
that works for square matrices only ;)
As Idakwo William said, you can use the basket weave method for the 3x3 matrix. If the determinant = 0 > its not linearly independent. If det doesn't = 0 > its linearly dependent
bur lapse other way around...if determinant is equal to zero, its linearly Dependent
nj weimer fixed it xD thanks
Thank u for saving my 2 remaining braincells's life
First time I watched your videos was in the 8th grade, when I was teaching myself calculus over the summer. I still find myself watching you in college when I need to review over a topic or get some practice. Thank you for all that you do, Patrick! You're changing peoples' lives, so cheers to that
Anyone watching this video in 2024!!?
Here 😂
Here..😂
Here😅
Me doing math in campus
Here, my exam will start in 1 hour 😂
Juste what i was looking for, thank you very much.
Such a good tutorial, even 9 years later. Thanks!
I love it when my professor just decides to never show up, and still took the test as if he had been there, I literally only have a table of contents and TH-cam
patrick jmt!!! you've helped me all throughout high school and college!! you rock my dude
I've commented this about 1000 times in your videos, but God Bless You!!
Simple explanations for simple concepts. My teachers somehow managed to make this convoluted. In 15 minutes you explained more than they did in 2+ hours. Kudos and much thanks:)
The real math teacher! Patrick!
Thank you for the video, but I think it is a long way, if you would like to find the case either is it linearly dependence or independence, you can find determinants. If determinants doesn't equal to zero , it means INDEPENDENCE, but if equal then DEPENDENCE (linearly.)
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You can find determinant for square matrices only. Here, it depends on problem whether we will be getting a square matrices or not.
Yes they do, but there is a difference between knowing the subject and being able to teach it. Patrick is a very skilled teacher, and has helped me a lot. :)
This is the third year that I have been referencing these math videos, and I must say you're a fantastic instructor!
I definitely credit you for developing my passion for math!
cheers,
Janice :)
Thank you Mr Patrick i remember about 10 years before when i was in 6th or 7th grade i have studied alot of exponential powers from your videos and now studying the concept of linear independence to pass my data science certificate i wholeheartedly respect you ... i am glad you still make videos for the students hope you are in good health :)
You're the best!!! I have passed soooo many classes solely because of your videos.
glad i could help you out :)
Thanks for making these videos! I'm taking matrix algebra right now but I got a little behind. Your videos have helped me catch up! They're well made and you explain things well
you have no idea how much this helps. thanks!!!!
I absolutely love your videos, they are incredibly informative and helpful! Thanks a ton Patrick!
Ur lectures is helping me in my take home IA right now.
Thank you very very much, your videos helped me a lot in my studies.
Thank you for this and everything else that you do. You just allowed me to ace my midterm. :)
GodBless! (if that's the kind of thing you believe in)
May the universe be kind to you.
You are the best math teacher.
I m truly impressed with ur English ....n you explain so well
Thanks so much for your tutorials! You break it down well, easy to understand the concepts.
Thanks, not only did you help me understand linear dependence you helped me to understand that I didn't understand how to properly reduce a matrix. I really thought I knew that! Guess that explains my last test grade
I started watching his vids in freshman year high school, now I am a freshman in college
Thank you so much Patrick! Your videos saved my ass for so many times!
+Monty Wu Really????
Man... You deserve more credit you are the man!!!
here I am, a 22 year old, watching this after 13 years of posting. Crazy to think about!
haha, here i am replying to it 13 years after making it :)
I have a linear algebra and vector geometry final in 2 days this is great review
guess who is watching this after 12 years later. ME
Yeh it is crazy math has not changed in 12 years.
Same here 😅
god dayum very well explained! my professor has very low energy and its monotoned so I always come back to ya when need help! thx
epic door creek
Appreciate you G, you make the most useful videos for the subject.
I am from germany and can' t speak so good english but your ideas are very good! I understand it! :)
By the way Patrick is the reason why I have been getting through engineering school, If you guys really do love him that much I suggest donating to him! He has a website and tbh he deserves it!
$1/mo on Patreon and I would sincerely appreciate it. But why buy the cow when you can get the milk for free? :)
LOL xD If you say so!
Ur video lecture has really helped me alot for my exams.Thanks alot............
this guy is the greatest of all time
appreciate your work, it`s very useful!
Thanks, Mr.Patrick
You're saving my life !! Thank you so much!!!! Your videos are awesome!
Dude you are amazing gonna love this video
Thank you very much King, you helped me to solve my problem you are very good in explaining
i heart you. so much. finals would suck if you didn't do what you do.
You sir are a gentleman and a scholar.
Thank you for helping me to pass our periodical test
Well explained
my man, again, lots of good stuff, lots of energies in your teaching. very good stuff
Things become easy for your help 🙏🙏
you also check by solving determinant.if the determinant is zero(0) then it will be dependent otherwise independent
Just what i was looking for! Thanks
Excellent I am 101 percent satisfied easy method by you thank you sir you will our maths professor in gju university
And again PatrickJMT saves the day :> thanks a lot sir!
thank the math gods for this video. was learning this in lecture today and i had no idea what was going on D:
Watched the first one and a half minute, and got exactly the answer I was looking for. :D
Yes!!!! I knew I could depend on pat! Another great video!
You're a lot better than my college professor.
Dude thanks man, Now I dont have to sit in class staring at the board confused, like if my teacher is doing magic
I will support u when I finnish my education in 5 years and become rich. But right now I need to support myself. xD Love your videos! Keep up the good work! :)
Great work bro, I really appreciate your work, this lesson was very useful.
thanks sir, i have learned almost 100% linear independence and dependence..............
I got this video in my recommended today. But I used your great videos to get through lots of math and chemistry classes. I missed you PatrickJMT and I'm glad I found you again
welcome back my friend :)
Is someone on a quest to dislike every Patrick video? I just cannot imagine anyone not liking and getting a better understanding after watching his videos.
His voice is amazing.
probably should of watch this video before my specialist maths exam
@afiqjenoba well, i hope a student of linear algebra would grasp that : ) and i emphasis that any value of k gives a solution, so it should be pretty clear i think to anyone listening!
Man I'm so relieved.
Excellent videos, I always wonder who the losers are who give these videos thumbs down
Disgruntled professors
David Field kids who are dumb and still don't get it
You have answered it David. "Losers!!".
Not everybody learns the same way.
you have saved my life soooooo many times
Thanks for the video. I must say it was helpful.
Turgut, i think you are totally right, in this case you can use the determinant and get the answer. But what about if it wasn't a 3*3 Matrix, then you have to go Patricks way, and i actually think it's better to learn Patricks way from the beginning :)) But you are 100 % right you can use the determinant in this case. :)
everything goes easy when you teach
So helpful thanks dude
thank you my dude. legend.
@Usagimusical glad i could help : )
3*3 Matrix , in this case, you shoul finde rank of matrix, if rank of matrix smaller than number of variables, it means linearly dependent, but if rank of matrix equal or greater than number of variables , then linearly independant
Good explanation.
Thanks
Excellent sir
@GreatTemplar glad i could help : )
ty so much I learned a lot from here.
He associates a1, a2, and a3 with a new variable, k, to show that there are infinitely many non-trivial solutions to the set of equations described by the matrix. Not only does this prove that the set of vectors is linearly dependent, but a set of solutions is described by [a1=(-1/2)k, a2=(-5/8)k, and a3=k] for which k can be any real number. If you plug any real number in for k, find the associated a1, a2, a3, and plug these into your definition of linear (in)dependence the result will be zero.
You are true hero, thank you!
ugh answered my question in 47 seconds.... THANK YOU
I'm chuckling right now at how simple this really is when he presents it 🤧
Why are youtube teachers ALWAYS better than our university professors?
because they are getting high salary from TH-cam 😂😂
Thank you Patrick !!!
God Bless you, sir.
Why u just dont compute the determinant of the matrix. If the answer is 0, that means they are linearly dependent.
+Mevlan Isufi At 5:00 why he is getting zero on the 1st row 2nd column? Does anyone know that?
+Dora Dağlaraşar He is trying to reduce it, to become the identity of a 2 x 2 matrix
+Marwa AlRuzaiqi thanks man, actually my exam was passed but still thanks.
No problem, hope you did good :)
You can only find the determinant of a square matrix, and not every matrix you come across will be nxn.
@afiqjenoba i am not sure i understand. since the equation has solutions for nonzero values of at least one of: a_1, a_2, a_3 (i show this generically by using the ' k ' notation ) we can say it is linearly dependent.
thank youuu excellent explanation
Thank you, you're a blessing!!!!
very helpful and clear！thank you
thanks patrickJMT .
have a test soon yay for this vid.
i didnt get how did you take a3=0. rest was reall help. you deserve gold medal.
thanks bro its help me much
if you see a free variable doesn tthat automatically mean linearly dependent
could you explain it without using the word vector and with no equations? Conceptually can't this be explained simply in a few sentences so non-mathmaticians can understand it?