⭐️ Learn more: ru-vid.com/group/PLKp3X-578hN8s5htUiN-8yO38BR4eaPsb ⭐️ Table of Contents ⭐ (0:00) Linear Algebra - Systems of Linear Equations (1 of 3) (16:20) Linear Algebra - System of Linear Equations (2 of 3) (27:55) Linear Algebra - Systems of Linear Equations (3 of 3) (47:18) Linear Algebra - Row Reduction and Echelon Forms (1 of 2) (54:49) Linear Algebra - Row Reduction and Echelon Forms (2 of 2) (1:4:10) Linear Algebra - Vector Equations (1 of 2) (1:14:05) Linear Algebra - Vector Equations (2 of 2) (1:24:54) Linear Algebra - The Matrix Equation Ax = b (1 of 2) (1:39:21) Linear Algebra - The Matrix Equation Ax = b (2 of 2) (1:44:48) Linear Algebra - Solution Sets of Linear Systems (1:57:49) Linear Algebra - Linear Independence (2:11:20) Linear Algebra - Linear Transformations (1 of 2) (2:25:10) Linear Algebra - Linear Transformations (2 of 2) (2:39:19) Linear Algebra - Matrix Operations (2:56:24) Linear Algebra - Matrix Inverse (3:12:17) Linear Algebra - Invertible Matrix Properties (3:24:24) Linear Algebra - Determinants (1 of 2) (3:44:40) Linear Algebra - Determinants (2 of 2) (4:04:28) Linear Algebra - Cramer's Rule (4:18:20) Linear Algebra - Vector Spaces and Subspaces (1 of 2) (4:48:30) Linear Algebra - Vector Spaces and Subspaces (5:13:13) Linear Algebra - Null Spaces, Column Spaces, and Linear Transformations (5:33:25) Linear Algebra - Basis of a Vector Space (5:59:43) Linear Algebra - Coordinate Systems in a Vector Space (6:15:41) Linear Algebra - Dimension of a Vector Space (6:26:35) Linear Algebra - Rank of a Matrix (6:50:09) Linear Algebra - Markov Chains (7:09:23) Linear Algebra - Eigenvalues and Eigenvectors (7:32:03) Linear Algebra - Matrix Diagonalization (7:49:08) Linear Algebra - Inner Product, Vector Length, Orthogonality
Wish I could thank you in person. The amount of care you gave by explaining small details and giving simple examples for the listeners is incredible and truly inspiring.
I have completed the whole theory of this course in about 9 days. I've had a bit of practice in the past when I was in college. This has been a great refresher and my basics are far more clear and thanks for providing such an awesome series of lectures, Dr. Betty Love.
@@projectpiano5231 iif he is rlly 12 that would be fantastic, but I hope you understand that their are a lot of trolls on the internet and that this is probably one of them. Otherwise there is no need for a 12 year old that flex on us like that :p. Anyways Let's just end the conversation
I do not ever comment on youtube videos. Ever. But I have got to take a moment to say thank you. I have a horrid Lin. Algebra professor who I am convinced genuinely does not care if myself or other students learn or not. I was on the verge of getting my first B in a math course even with reading the book myself but now that I have this video I really think I can pull off an A in the class. You have no idea how much this means to me, this is going on my transfer transcripts. Seriously, thank you. UPDATE: I got the A!!! Thanks again!
you have people dancing like idiots and getting millions of views then you have people like this doing their best to actually present something useful for society and not waste other people’s time with useless trends, with under 100k. This deserves all the views.
What made you feel the need to make this comment? You could've just complimented the video without bringing shit people find funny down lmao. Just because your life is boring doesn't mean you need to project it onto this video jesus.
There's a philosophical film about Apocalypse. In that film, a professor raises this question. Should we save only scientists and other "useful" people and let dancers, artists etc. die? It's an interesting film.
Just finished the video, took notes and tried to understand all of it conceptually over the course of I think 4 days. Thank you soooo much for such a great resource! It genuinely helps.
I want to mention that at the beginning of this video they say that b is "is the right had side value". They should have said that b is a constant. It does not matter whether or not the b is on the left hand or right hand of the equation.
I had a terrible instructor for this class. I still got an A, but after watching parts of this video I've learning the pieces I was missing. Also this video is spot on for all the class encompassed, although I didn't see isomorphism.
You have made my Linear Algebra course feel like a breeze with your method of teaching, especially knowing my current professor, despite knowing the content, is extremely bad at explaining. I really appreciate your hard work, thank you! The use of colour is extremely efficient at learning, which I'm glad you incorporated, especially at 3:29:00
Dear Professor, I would like to extend my thanks for the outstanding videos you have shared. They have been immensely beneficial. I am looking forward to further practice and enhancement of my skills. Could you kindly inform me about the book you reference in the videos? I wish to tackle additional problems for practice. Thank you once more for your invaluable resources.
I wanted to learn linear algebra course in RU-vid because I'm not understanding well to that course. Now I'm feeling better after listening your that amazing and wonderful, easy to understand tutorial.. about linear algebra.. I'm from Pakistan.... Really Really lovely to understand... Thanks for providing me helpful video.... best regards and wishes from me... Thanks 🌹🌹❤️❤️💕
Awesome Farhan! Keep up the good work. It's cool to think of a person across the other side of the world learning and struggling with the same maths I am! With much sincerity from California
I appreciate the effort made here to educate the masses...that is the Utube watchers. The negative for me in this presentation is the infinite series of 'um', 'uh', and 'so'. I associate these time stealers with a lack of preparation for or fluidity of the subject I read some of the comments, so it seems there are those who benefit...um, I see that as an indication to continue your positive work. Best wishes
Ok I don't really comment on math videos. But this shit is my life savor. I am taking linear algebra on next quarter. It took for a week to understand just 1.1 for me on my own. However I finally got an idea thanks to this prof. The best thing is I am gonna use the exactly same textbook on next quarter. Thank you so much
I basically knew everything but the last hour already (I don't think we spoke about this), but this video was extremly helpful anyways. It gave me visual examples to remember everything by and most of all, it made it clear to me that I actually know the stuff, thats the exam about. Im writing my exam tomorrow and this video helped me a lot with my mental. :)
This is a great course. Explaining difficult concepts in such a relaxed way is not given. You are very talented. Thank you. I have one question though: I don' t understand the slide at 7h:12min:52s why (A - Lamda*I ) need not be invertible ? or (A - Lamda*I )*x has non trivial solutions ? for the eigenvalue/eigenvectors to be defined..... in other words what happens if (A - Lamda*I ) is invertible ?
@@theoreticalphysicistzeinaq2753 Magnificent!! Learning these concepts at 12 years of age is truly brilliant ! Yet there's a lot to discover so keep learning !!
Thanks for the time you're taking to do this. Please take time to explain. Don't just state, brush over and assume we know or understand. This course had the potential to really help me but I still don't understand 🥺
@@dhruvamin197 that also happened to me the first time 😅, it's normal because linear algebra is very abstract (more than calculus), the part I got most confused at first is the video about linear transformations, but after I watched it three/four times and digested the topic, all the others topics were easier to understand because they are all based on that (determinant, basis, subspaces, rank, eigenvalues, etc.),
At 2:03:40, how can it be linearly dependent for having no free variable, while having none of the vectors in the set be a multiple of another within that set? Or is that strictly for when there are only two vectors in a set?
There are 3 vectors in 2 dimensions(each vector has only 2 elements). This can also said as 2 equations and 3 unknowns. Because there are 2 equations, the 3rd unknown will always be a free variable even thought none of the vectors is a multiple of any of the other vector in the set. Look at the other way, for this set of vectors to not have a free varible there are 2 conditions to be met. a. Any vector is not a multiple of any of the other vector b. the number of unknowns and number of equations or number of unknowns and number of elements(dimensions) in a vector should match. You mentioned no free variable, in fact there is a free variable(for the 3rd unknown and the same can be worked out) and hence the 3 vectors are linearly dependent.
its a nice this course but i think everybody will need to try to read a book oflinear algebra after this video xD to improve thier skills solving the books problems xD
In physics vectors have unit but in maths everywhere i see there is no unit. Aren't vector physical quantity that have magnitude n direction. And physical quantities have units ( SI units n all ) But when I was studying in maths vector just had magnitude n direction no unit
In physics vectors have unit but in maths everywhere i see there is no unit. Aren't vector physical quantity that have magnitude n direction. And physical quantities have units ( SI units n all ) But when I was studying in maths vector just had magnitude n direction no unit
Does this course contain the basics of sets, relations, recurrences, simple combinatorial problems, Matrices and basic matrix algebra? Someone, please answer.
In physics vectors have unit but in maths everywhere i see there is no unit. Aren't vector physical quantity that have magnitude n direction. And physical quantities have units ( SI units n all ) But when I was studying in maths vector just had magnitude n direction no unit
Hey can you please tell whether this course is a college course or a school course? Because in school also some basics of matrices was taught, but please let me know whether this linear algebra course is for school or college.
Hi, @ 2:09:13 - why do you switch the signs to prove that vector -3 2 isa linear combination of 1 4 and 2 1 ?? I dont understand how you go from top equation to below one.... thanks
They took the two vectors to the right hand side and hence switched signs Like this: Say *v1* , *v2* & *v3* are the vectors. We have *v1* + *v2* + *v3* = *0* in the above equation Now after re-arranging , *v3* = - *v1* - *v2*
In physics vectors have unit but in maths everywhere i see there is no unit. Aren't vector physical quantity that have magnitude n direction. And physical quantities have units ( SI units n all ) But when I was studying in maths vector just had magnitude n direction no unit
Your work is good. Appreciated. If you contact me I could share another method/ alternative method of solving linear equations, (simultaneous equations) apart from the known elimination and substitution. Nearly to be published very useful and more accurate, self proval easy to understand.
It doesn’t. Some people using machine learning to predict the market made a fortune, but also some people lost a fortune. Some systems perform well for some time and then suddenly start losing. The day you can predict the market, they’ll shut it down.
25:18 - the common substitution/elimination method with the original two equations without the right hand side (17:15) is simple and direct to solve the system, why then bother to make it complex by using the other unnecessary tricks?
