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.
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
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
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?
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" 😉
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
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:)
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
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.) BEST REGARDS FROM AZERBAIJAN
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 :)
@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!
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
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.
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
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!
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.
@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.
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! :)
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. :)
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
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
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?
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.
Hey patrick, First off, I love your videos, they explain a lot in simple terms. Also, why does a3 = K? wouldnt a3 be multiplied by 0 and thus result in zero? I don't understand why that is done :S can someone please point me in the right direction? What does he mean by free variable k? and why does a3 = k, why not a2 or a1?
Great video, just a question though. When you found the all-zero row couldn't you stop and say that vectors are linearly dependent? (all-zero row -> infinite solutions)
i love your videos and u have helped so much thanks!, but i cant seem to figure out to do if you have variables in some of the spots of the matrices how do you find what makes it a linearly dependent or what makes it a linealy independent? i got a test monday im freaking out plzz helpppp
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
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
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 😂
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:)
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
Such a good tutorial, even 9 years later. Thanks!
Juste what i was looking for, thank you very much.
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.)
BEST REGARDS FROM AZERBAIJAN
You can find determinant for square matrices only. Here, it depends on problem whether we will be getting a square matrices or not.
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!!
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 :)
The real math teacher! Patrick!
You're the best!!! I have passed soooo many classes solely because of your videos.
glad i could help you out :)
you have no idea how much this helps. thanks!!!!
@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... You deserve more credit you are the man!!!
You are the best math teacher.
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
I absolutely love your videos, they are incredibly informative and helpful! Thanks a ton Patrick!
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.
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.
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
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 :)
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.
@patrickjmt at 5:01 why should you have a zero in the first row, second column?
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!
I have a linear algebra and vector geometry final in 2 days this is great review
I am from germany and can' t speak so good english but your ideas are very good! I understand it! :)
Ur video lecture has really helped me alot for my exams.Thanks alot............
I m truly impressed with ur English ....n you explain so well
this guy is the greatest of all time
Excellent I am 101 percent satisfied easy method by you thank you sir you will our maths professor in gju university
Thanks so much for your tutorials! You break it down well, easy to understand the concepts.
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
Thank you so much Patrick! Your videos saved my ass for so many times!
+Monty Wu Really????
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.
Dude you are amazing gonna love this video
Thank you for helping me to pass our periodical test
You're saving my life !! Thank you so much!!!! Your videos are awesome!
i heart you. so much. finals would suck if you didn't do what you do.
appreciate your work, it`s very useful!
@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.
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! :)
please tell how did u get negative four 5:40
my man, again, lots of good stuff, lots of energies in your teaching. very good stuff
Watched the first one and a half minute, and got exactly the answer I was looking for. :D
epic door creek
I started watching his vids in freshman year high school, now I am a freshman in college
Appreciate you G, you make the most useful videos for the subject.
And again PatrickJMT saves the day :> thanks a lot sir!
you have saved my life soooooo many times
Dude thanks man, Now I dont have to sit in class staring at the board confused, like if my teacher is doing magic
Yes!!!! I knew I could depend on pat! Another great video!
thank the math gods for this video. was learning this in lecture today and i had no idea what was going on D:
Thank you very much King, you helped me to solve my problem you are very good in explaining
You're a lot better than my college professor.
You sir are a gentleman and a scholar.
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. :)
Things become easy for your 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
Why are youtube teachers ALWAYS better than our university professors?
because they are getting high salary from TH-cam 😂😂
Well explained
Just what i was looking for! Thanks
Here poh hahahhha now lang topic kopoh kasi yan😅😅😅😅
Great work bro, I really appreciate your work, this lesson was very useful.
thanks sir, i have learned almost 100% linear independence and dependence..............
Thanks, Mr.Patrick
you also check by solving determinant.if the determinant is zero(0) then it will be dependent otherwise independent
guess who is watching this after 12 years later. ME
Yeh it is crazy math has not changed in 12 years.
Same here 😅
@afiqjenoba no, no i do not think you were undermining my explanation at all : )
His voice is amazing.
Thanks for the video. I must say it was helpful.
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 :)
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?
@Usagimusical glad i could help : )
everything goes easy when you teach
if you see a free variable doesn tthat automatically mean linearly dependent
what would be the coefficient of dependence of the column vectors of that matrix. I am having a lot of trouble finding how to do this.
ugh answered my question in 47 seconds.... THANK YOU
I'm chuckling right now at how simple this really is when he presents it 🤧
how would you do it, if they gave gave you a set of vectors of 2x2 matrices.
probably should of watch this video before my specialist maths exam
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.
Hey patrick, First off, I love your videos, they explain a lot in simple terms.
Also, why does a3 = K? wouldnt a3 be multiplied by 0 and thus result in zero? I don't understand why that is done :S can someone please point me in the right direction?
What does he mean by free variable k? and why does a3 = k, why not a2 or a1?
Guess who is watching this after 13 years later. ME
what if a question of eight 3x3 matrices asking about which one is indep
how to solve it fast when you still have 14 other questions.
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.
what if you're given something like p1=1, p2=x and p3=x^2 in p2 how can you form matrices with those?
how do you determine to use 2R_1 + R2 -> R2? is that just standard procedure or is there a step
putting into Row Echelon form by using row operations
finally someone with a great voice!
Racist
Great video, just a question though. When you found the all-zero row couldn't you stop and say that vectors are linearly dependent? (all-zero row -> infinite solutions)
You are true hero, thank you!
From which book you took this question ? Kindly reply it will mean a lot
i love your videos and u have helped so much thanks!, but i cant seem to figure out to do if you have variables in some of the spots of the matrices how do you find what makes it a linearly dependent or what makes it a linealy independent? i got a test monday im freaking out plzz helpppp
How'd the test go?
@@SPARTAN26MiLLiX brooo i dont know whether this was supposed to be funny but its really cracking me up this night.🤣🤣🤣
@@doommood9911 Only a five year gap after the test. I'm sure he still remembers.
@@transfo47 6 years now.....
So helpful thanks dude