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 UA-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?
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
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
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
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 UA-cam
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 :)
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
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:)
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 :)
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. :)
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!
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
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
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. :)
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.
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.
@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!
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)
@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 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
Hey in my mathematics book it written like "if the Eigen values are non-repeated then then it has linearly independent Eigen vectors". But my say on this is : " If they are non-repeated then how is it linearly independent because all the Eigen values must be zero in a linearly independent combination. Thanks in advance :)
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?
When we say vectors are LI then it means every scalar associated with vectors are zero and we also know that these scalar belongs from field F and field must be abelian group with respect to multiplication so it is obvious that it will follow property of *existence of inverse*. But 0 has no multiplicative inverse. Then how these scalars (which are zero) can be elements of a field ? 😢
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 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 UA-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)
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
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
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.
Anyone watching this video in 2024!!?
Here 😂
Here..😂
Here😅
Me doing math in campus
Here, my exam will start in 1 hour 😂
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 UA-cam
Juste what i was looking for, thank you very much.
patrick jmt!!! you've helped me all throughout high school and college!! you rock my dude
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 :)
I've commented this about 1000 times in your videos, but God Bless You!!
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
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:)
Ur lectures is helping me in my take home IA right now.
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 :)
you also check by solving determinant.if the determinant is zero(0) then it will be dependent otherwise independent
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 :)
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. :)
You're the best!!! I have passed soooo many classes solely because of your videos.
glad i could help you out :)
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!
Well explained
The real math teacher! Patrick!
Thank you very very much, your videos helped me a lot in my studies.
I have a linear algebra and vector geometry final in 2 days this is great review
Things become easy for your help 🙏🙏
You sir are a gentleman and a scholar.
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
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
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. :)
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 for helping me to pass our periodical test
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 have no idea how much this helps. thanks!!!!
Thanks, Mr.Patrick
epic door creek
I am from germany and can' t speak so good english but your ideas are very good! I understand it! :)
I absolutely love your videos, they are incredibly informative and helpful! Thanks a ton Patrick!
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.
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.
Thank you so much Patrick! Your videos saved my ass for so many times!
+Monty Wu Really????
@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!
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
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)
Thank you very much King, you helped me to solve my problem you are very good in explaining
guess who is watching this after 12 years later. ME
Yeh it is crazy math has not changed in 12 years.
Same here 😅
Why do we want to 0 out the number in row 1 column 2? it was the last matrix operation you did before determining the non-trivial solutions.
I started watching his vids in freshman year high school, now I am a freshman in college
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.
Appreciate you G, you make the most useful videos for the subject.
You are the best math teacher.
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.
this guy is the greatest of all time
Man I'm so relieved.
Man... You deserve more credit you are the man!!!
if you see a free variable doesn tthat automatically mean linearly dependent
@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.
Just what i was looking for! Thanks
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 :)
appreciate your work, it`s very useful!
You're saving my life !! Thank you so much!!!! Your videos are awesome!
Excellent sir
i heart you. so much. finals would suck if you didn't do what you do.
@patrickjmt at 5:01 why should you have a zero in the first row, second column?
thanks sir, i have learned almost 100% linear independence and dependence..............
Thanks for the video. I must say it was helpful.
Hey in my mathematics book it written like "if the Eigen values are non-repeated then then it has linearly independent Eigen vectors". But my say on this is : " If they are non-repeated then how is it linearly independent because all the Eigen values must be zero in a linearly independent combination. Thanks in advance :)
everything goes easy when you teach
Good explanation.
Thanks
God Bless you, sir.
His voice is amazing.
Thank you Patrick !!!
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?
You're a lot better than my college professor.
thanks patrickJMT .
You are true hero, thank you!
So, can we say that independent matrices have unique solution?
Great work bro, I really appreciate your work, this lesson was very useful.
so since there's a row of entirely zeros, you could say that the vectors have an infinite amount of solutions?
Sir would be please solve: Find A(W), Where W is spanned by (1,2,3) and (0,4,-1)
Dude you are amazing gonna love this video
@Usagimusical glad i could help : )
From which book you took this question ? Kindly reply it will mean a lot
probably should of watch this video before my specialist maths exam
clean and clear ....thanks
since this is a square matrix we can find the determinant of the matrix.
it comes out to be 0.. which also confirms that it is Linearly dependent..
A = [2 4 6;7 5 3;1 4 6];
B = [2 4 6; 7 5 3;4 8 12];
Find the linear dependent and linear independent rows in the matrix A and B????
my man, again, lots of good stuff, lots of energies in your teaching. very good stuff
shouldn't the conversion from vector to matrix be done differently ?
I mean column 1 should have been
1 , 4 , 3
and not
1, -2, 0 ?
thank you my dude. legend.
have a test soon yay for this vid.
Yes!!!! I knew I could depend on pat! Another great video!
So helpful thanks dude
When we say vectors are LI then it means every scalar associated with vectors are zero and we also know that these scalar belongs from field F and field must be abelian group with respect to multiplication so it is obvious that it will follow property of *existence of inverse*. But 0 has no multiplicative inverse.
Then how these scalars (which are zero) can be elements of a field ?
😢
ty so much I learned a lot from here.
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.....
thank you so much!!, it really helps. I am just wondering if you can do a video on LU factorization too?