Linear Algebra 1.1.1 Systems of Linear Equations

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  • Опубліковано 6 лют 2025

КОМЕНТАРІ • 266

  • @krizh289
    @krizh289 2 роки тому +678

    It's outrageous that colleges still demand around $2k for a class which I can learn completely free online because of educators like you. Thank you, hopefully I pass the final

    • @SawFinMath
      @SawFinMath  2 роки тому +204

      I get it. But my students do pay $2k to take my classes.

    • @davidcabreramartinez4892
      @davidcabreramartinez4892 2 роки тому +23

      UA-cam does not get you a title fellow

    • @minnil7927
      @minnil7927 2 роки тому +37

      @@SawFinMath at northwestern university im paying around 6k for this class. you are far better than my calc prof already. I take it next term so I am hoping I can get a head start here!

    • @krizh289
      @krizh289 2 роки тому +20

      @@davidcabreramartinez4892 Yeah, that's my entire point. Education should be free and it's bad that we have to pay thousands for a piece of paper even if we have the knowledge

    • @panpan5341
      @panpan5341 2 роки тому +8

      I believe the payment is just so that you could have the credit towards a degree. A lot of college campuses are public so you can just walk in and sit down for a class. Unfortunately, colleges just operate like a business and care more about money than the education.

  • @calamityesp609
    @calamityesp609 3 роки тому +33

    YOU ARE MY HERO!!! NOT ONLY SAVED ME IN DISCRETE MATHMATICS< YOU'RE SAVING ME IN LINEAR ALGEBRA AS WELL!!! WHAT!!!

    • @SawFinMath
      @SawFinMath  3 роки тому +5

      So glad I could help!

    • @eevibessite
      @eevibessite 2 роки тому

      ua-cam.com/video/0Ahj8SLDgig/v-deo.html

    • @harrasmansoor4098
      @harrasmansoor4098 Рік тому

      @@SawFinMathAre you teaching using David C Lay Linear Algebra book ?

    • @TejasviPradhyumna
      @TejasviPradhyumna 8 днів тому

      legit me. My linear alg teacher can't even teach

  • @falayyou
    @falayyou 4 місяці тому +9

    Massive respect for teaching this. You lost me after about 8 mins. I have no idea what was going on. But will have some coffee and have another crack tomorrow.

  • @jookeefee
    @jookeefee 3 місяці тому +2

    My professor beat around the bush and never really explained anything, but watching your video on 1.5x speed made me understand how these work, why they're useful, and how to do it. thank you so much for going out of your way to upload this, you are a lifesaver to me and I'm sure plenty of others.

  • @Th3BlackLotus
    @Th3BlackLotus 3 роки тому +14

    Going to college for the first time(16 years after I graduate HS). This is gonna be a life saver.

  • @yousufborno3875
    @yousufborno3875 5 років тому +73

    Ma'am, I am from Bangladesh. I am a big fan of your lectures. Even a layman can master any math topic from your lectures. Thank you so much for your wonderful and valuable content.

  • @rijaahmed4032
    @rijaahmed4032 2 роки тому +121

    My eyes are teary right now. I got 100/100 on linear algebra exam after learning from you!

    • @SawFinMath
      @SawFinMath  2 роки тому +21

      That makes me so happy! Great work!

    • @rijaahmed4032
      @rijaahmed4032 2 роки тому +1

      @@SawFinMath Thank you so much teacher!

    • @zainahmed546
      @zainahmed546 Рік тому +2

      Congratulations! did you prepare from a book as well or were these videos enough for you?

    • @rijaahmed4032
      @rijaahmed4032 Рік тому +2

      @@zainahmed546 these videos and also my university gave some notes so I studied those too

    • @zainahmed546
      @zainahmed546 Рік тому +1

      @@rijaahmed4032 fair enough. thanks

  • @123ucr
    @123ucr Рік тому +95

    As someone who has taken and passed Linear Algebra in the past, I must admit this math class is a fun and challenging and worthwhile math class especially for computer science. It is your first taste of abstract mathematics. While the calculations in Linear Algebra are tedious but straightforward (if you know the tricks), what makes this class a challenge are the proofs and some of the concepts (especially basis and dimension, linear dependence vs linear independence, subspaces, vector spaces, null and column spaces, eigenvalues vs eigenvectors, and so on). Also, my advice for people taking this class, "do not be fooled by the course title". This math class is not a high school level math class; it is at the university level. It is one of the reasons why many people do badly in this class is because they underestimate the difficulty of this class. In fact, it is normally taken at least after two semesters of Calculus and taken concurrently with Calculus 3/ (Multi-variable or Vector Calculus to be precise) and/or Elementary Differential Equations (two concurrent level math classes). Students need to develop the mathematical maturity (e.g. critical thinking and abstract reasoning) for Linear Algebra. Also, this math class prepares for higher level math classes (e.g. Abstract Algebra, Number Theory, Partial Differential Equations, etc.). Good luck to anyone taking this math class.

    • @rudyj8948
      @rudyj8948 Рік тому +3

      I took it and it was like you said, fun but challenging. This semester my DiffEQ class is combined with a Linear Algebra Class, so im absolutely crushing the LA bits lol.

  • @cringeworthybears5500
    @cringeworthybears5500 4 роки тому +66

    I appreciate this so much. Time to watch the entire series since my professor doesn't want to teach :D

    • @AwsTheBaws
      @AwsTheBaws 4 роки тому +2

      xd same reason im here and i cant read his hand writing, + hw due in 2 hrs >.

    • @shantanu925
      @shantanu925 4 роки тому +1

      Sameee, What's your college?

    • @mayvalley
      @mayvalley 4 роки тому

      Same for me!! Professor has terrible writing and is super unorganized and makes mistakes in his lectures

    • @SawFinMath
      @SawFinMath  4 роки тому +6

      Thanks! Glad I could help!

    • @rachelprojects7590
      @rachelprojects7590 4 роки тому +1

      @@mayvalley are you a Carleton student?

  • @legend7890
    @legend7890 4 роки тому +45

    Thank you very much. I learned more from you than I did from my professor. Today I had my final exam and made an A

    • @SawFinMath
      @SawFinMath  4 роки тому +9

      Congrats!

    • @harrasmansoor4098
      @harrasmansoor4098 Рік тому

      @@SawFinMathAre you teaching from the David C Lay Linear Algebra book ?

  • @TheHeroIsRisingUp
    @TheHeroIsRisingUp Рік тому +3

    So glad I found this. I wanted to learn Machine Learning but this math is required for me to grasp ML better.

  • @zawar_yt
    @zawar_yt Рік тому +10

    i've passed my Stats, Discrete math, and now linear algebra hopefully, just because of you.. i'm like really bad at math but you have incredible teaching skills.......

  • @julianayagyu6088
    @julianayagyu6088 2 роки тому +36

    Thank you so so much for making these videos! Before I was only copying the steps, but now I also understand the concept. You're a lifesaver!

    • @amrtaha3436
      @amrtaha3436 2 роки тому

      Can u help me to solve some equations?

  • @youreyesarebleeding1368
    @youreyesarebleeding1368 2 роки тому +2

    I can't understand my Linear Algebra professor's English at all, so I use this playlist instead, it's a big help.

  • @NA-cl6vj
    @NA-cl6vj 4 роки тому +47

    This was surprisingly easy and educative. You're a hero.

  • @lactran2979
    @lactran2979 6 місяців тому +5

    I recommend Howard’s book to those who want to challenge themselves with exercise and have a deep understanding of LA.

  • @obakengmothusi9149
    @obakengmothusi9149 Рік тому +3

    If there really is a God. I hope my thanx and good will reaches you somehow. You are an amazing teacher.

  • @dark.knight112
    @dark.knight112 Рік тому

    I am from Nepal, this is exactly the type of quality education I needed.

  • @bahar5517
    @bahar5517 Рік тому +3

    I don't understand anything from my proffessor thanks to you I understand everything clearly

  • @muhammedyasir2103
    @muhammedyasir2103 3 місяці тому +1

    I love you Kimberly.. ❣💋 best Linera Algebra course in the world.. Thank you...

  • @oneofmany31
    @oneofmany31 2 роки тому +3

    Since I have a exam tomorrow and It's 9pm
    It is now officialy the time,
    to speedrun entire 12 hours of this playlist.
    Winnable

    • @xbz24
      @xbz24 Рік тому

      How did it went doe

    • @oneofmany31
      @oneofmany31 Рік тому +5

      @@xbz24 I fell asleep and fail

    • @xbz24
      @xbz24 Рік тому +3

      @@oneofmany31 glad to hear that

  • @aizazahmed1637
    @aizazahmed1637 3 роки тому +2

    THank you for such an amazing playlist i scored 9 marks out of 150 and passed my course with a D grade. YOU ARE AMAZING 💘💘💘💘💘💘

  • @motivationbyanythingmba3334
    @motivationbyanythingmba3334 7 місяців тому

    I am part time worker and student thats why doing maths and other was really difficult but seems like youre lifesaver now i can go through all your videos it covers overall around 80% of maths i need to attend thanks mam🙏❤️

  • @simonndou7625
    @simonndou7625 Рік тому +6

    preparing for my linear exam your videos have been so helpful mostly the statistic series it helped me big time 💥🤝

  • @deema1737
    @deema1737 2 роки тому +1

    this playlist is saving my engineering degree

  • @SolomonOkomowho
    @SolomonOkomowho 6 місяців тому

    This was easy to understand. I was wondering why I would need to use a matrix to solve linear equations that I can do easy in my head until you said 5 or more equations. This is wonderful will definitely finish the course.

  • @gurpchirp
    @gurpchirp 2 роки тому +4

    fantastic teaching style. thank you so much. learning programming and was told to start with linear alg/ calculus.

  • @carley7227
    @carley7227 5 місяців тому

    i just had my first linear algebra 300 class today and my prof completely confused me, this helps a lot

  • @tickyotacky
    @tickyotacky 2 роки тому +2

    Man I wish my teacher explained it to me like this, or I wish I found this video earlier. Big props to you though, great quality and explanation.

  • @KAhmed_21
    @KAhmed_21 Місяць тому

    Thank you so much mam for these series. The way you teach is really appreciable. All your lecture videos are really helpful.

  • @zorkovroman9575
    @zorkovroman9575 Рік тому

    Thanks!

    • @SawFinMath
      @SawFinMath  Рік тому +1

      You are awesome! Thanks for the Super Thanks!

  • @aceofspades-ht7bs
    @aceofspades-ht7bs 3 роки тому +1

    This is our literal class.

  • @vew1915
    @vew1915 4 місяці тому +1

    Nah forever GOATed❤🔥

  • @THHatch
    @THHatch Рік тому

    it took my professor 3 x 50-minute lectures to barely teach this and I didn't understand it at all. To only 18 minutes and was completely able to finish the assignment that was given to me today for homework like I knew this professionally. Time is Money.

    • @SawFinMath
      @SawFinMath  Рік тому

      Goodness! Well be sure to bookmark the playlist if you are enrolled in Linear Algebra. Best of luck!

  • @aimeerohan8227
    @aimeerohan8227 2 роки тому +1

    Thank you for all that you do. My teacher goes off the "Thayer method" at my school where I have to teach myself before the class.

    • @SawFinMath
      @SawFinMath  2 роки тому

      That's gotta be a rough way to learn.

  • @kaylee3078
    @kaylee3078 3 роки тому +3

    when i say i couldn't figure this out earlier- thank you. math has me crying lol

  • @lifestyleam-k3d
    @lifestyleam-k3d 11 місяців тому

    As a student currently taking a linear algebra course, I have found Your explanations very useful. Thank You for explaining the concept in detail. If I could add something to the video, I would add examples where you solve problems and get a raw of 0 or some free variables in the solution set. That way, the examples will be more diverse. Moreover, what I find very useful is the practice exercise at the end, which strengthens the concepts discussed in the video.

  • @mmm_moon5989
    @mmm_moon5989 Рік тому

    Sitting at a 49% in the class but you're actually going to save my grade

  • @rugiyyahassanova7980
    @rugiyyahassanova7980 3 роки тому +3

    Im gonna write a comment bcz just wanna help your video to hit trends. Btw your lectures and explanation are GREAT . thank u so much. God bless you

    • @eevibessite
      @eevibessite 2 роки тому

      ua-cam.com/video/lOuKqOwsDgE/v-deo.html

    • @eevibessite
      @eevibessite 2 роки тому

      ua-cam.com/video/0Ahj8SLDgig/v-deo.html

  • @HaisumHaroon-s6i
    @HaisumHaroon-s6i 10 місяців тому +1

    Your videos seem to be great! Can you please tell in which lecture have you covered particular solutions, special solutions and complete solutions. I am unable to find so that would be really helpful!

  • @Mo-Fozi
    @Mo-Fozi 10 місяців тому

    thx ♥

  • @travis.miller
    @travis.miller 6 місяців тому +1

    I don't neccissarily have the best brain when it comes to math but watching this a couple times and following along has definatley helped. Thank you. Do you recommend any practice problems one could try?

  • @SitiZulaikha-j4n
    @SitiZulaikha-j4n Рік тому

    AH THANK YOU SO MUCH! I REALLY NEED THIS. YOU ARE MY LIFE SAVER. LUV U THANKYOUUUUUUU

  • @LeisureSuitLaurent
    @LeisureSuitLaurent Рік тому

    Textbook: David Lay Linear Algebra and Its Applications 7e
    Aww, wish you were using Larson. I got 91/93 in Discrete 1/2 from your Rosen-based lectures! Thanks!

    • @SawFinMath
      @SawFinMath  Рік тому +1

      My new playlist uses Larson, but I only have one video done so far

    • @LeisureSuitLaurent
      @LeisureSuitLaurent Рік тому

      @@SawFinMath Thanks! I see it. Since my course is active, am I fine going through this list here, or are there significant differences between the two?

    • @SawFinMath
      @SawFinMath  Рік тому +1

      The new list will cover all sections, including Markov chains, etc. I also feel the sequence of topics lends itself better to understanding the ‘why’ and not just the ‘how’. But nothing wrong with the original series.

  • @DirectedByMichaelBay
    @DirectedByMichaelBay 2 роки тому +1

    Thanks I think I can pass my 5/6 test

  • @danialahmed3005
    @danialahmed3005 4 роки тому +1

    Life saver, your the got thank you so much. Im in second year and my prof cant teach anything

  • @alaaddintimez1887
    @alaaddintimez1887 Рік тому +1

    I liekd this videyo, it taot me how to oslve my homework. THa!

  • @dipanshgarg9981
    @dipanshgarg9981 Рік тому +1

    that "oops, forgot my x" was at 6:23 personal 😂.

  • @Ariobarzanes113
    @Ariobarzanes113 Рік тому +1

    Thanks a lot !

  • @moth36
    @moth36 4 роки тому +4

    Very clear explanation , thank you very much

    • @eevibessite
      @eevibessite 2 роки тому

      ua-cam.com/video/0Ahj8SLDgig/v-deo.html

  • @Mathematicsketeacher
    @Mathematicsketeacher Рік тому

    very helpful and infromative

  • @aminaelassri8873
    @aminaelassri8873 5 місяців тому +1

    thank you!

  • @musfiratalha4656
    @musfiratalha4656 2 роки тому +1

    Thank you kimberly!

  • @ashishpatil5251
    @ashishpatil5251 9 місяців тому

    Very soothing and sweet voice

  • @dantex9083
    @dantex9083 17 днів тому

    Cool stuff. What textbook are you using for this course?

  • @shimaalcarrim7949
    @shimaalcarrim7949 Рік тому

    Teacher is amazing

  • @kend9a
    @kend9a 16 днів тому

    Hello Prof BREHM. I follow your course from TAIWAN, Thanks for this amazing course. I wanna know if you don't have a worksheet for this course. it would be amazing if we can have it

  • @JZ8_
    @JZ8_ Рік тому

    A true life saver, thank you so much 🙏

  • @TusharDeb23
    @TusharDeb23 11 місяців тому +2

    What is the textbook being used for this course?

  • @skinnycucumber
    @skinnycucumber Рік тому

    thank you Professor Brehm!

  • @StaticBlaster
    @StaticBlaster Рік тому

    Even though I have three years of college behind me, who needs college? It's the experience that matters anyway. Imagine watching videos on calculus 1-3, ode's, linear algebra, circuit analysis 1-2, signals and systems, digital logic, computer architecture, software design patterns, programming in C++ and python, microcontrollers and buying DIY electrical/computer/Arduino kits to simulate a lab environment. That could probably get you a job if you're ambitious enough.

  • @samuelomondi6073
    @samuelomondi6073 Рік тому

    great work,,,thanks

  • @TreeBear-c8l
    @TreeBear-c8l Рік тому

    wow , really helpful, thank you

  • @moneymachine6836
    @moneymachine6836 4 місяці тому

    I can't understand my linear algebra teacher at all. She never starts the question from scratch, and when she does problems she goes from problem 4 to 11 then back to 4. Really glad I found this course. Just out of curiosity, what textbook is being used?

    • @SawFinMath
      @SawFinMath  4 місяці тому

      David Lay. But I’ll be starting a new series including more topics using Larson

  • @peyton9635
    @peyton9635 Рік тому +1

    paying 2k for a class when all my professor does is send this video. thanks.

    • @SawFinMath
      @SawFinMath  Рік тому +1

      That's awful. You can send me your 2K instead :) Kidding. But hopefully between myself and your professor, you can both learn Linear!

  • @micah2936
    @micah2936 Рік тому

    Been wanting to take this class so bad but I don’t have the time with work and family.
    I feel like this is a puzzle piece missing from my brain to connect me to many concepts.
    I took differential equations before this class not knowing it existed first lol

  • @MaxScince
    @MaxScince Місяць тому

    Thanks for the video

  • @JR1481M1
    @JR1481M1 4 роки тому +3

    Where did she get 1/5 from? I don't see it

  • @pandaonsteroids5154
    @pandaonsteroids5154 Рік тому

    Very good.

  • @rennaafi_
    @rennaafi_ 2 роки тому +2

    Thx a lot 🤩

  • @_dream_big
    @_dream_big Рік тому +2

    Could you please mention the name of the book in case you followed any for this course.

    • @Et3rna12un2h1ne
      @Et3rna12un2h1ne 8 місяців тому

      It's based on Linear Algebra and its Application by Lay. 😊

  • @briefcasemanx
    @briefcasemanx 8 місяців тому

    Nice. Is this (the ordering of subjects) based on Lay's book?

  • @jewel_throne2950
    @jewel_throne2950 4 роки тому +1

    Amazing

  • @Pete-da-peter
    @Pete-da-peter Рік тому

    Lesson completed! Horray

  • @Ryan-mw9pm
    @Ryan-mw9pm 5 місяців тому

    Thank you teacher!

  • @kauserahmed6669
    @kauserahmed6669 7 місяців тому +1

    ma'am, please tell me. who is the writer of the book and edition?

  • @youtubeexpert2441
    @youtubeexpert2441 Рік тому +1

    6:24 when i finally meet the right one

  • @ashleypoblano2100
    @ashleypoblano2100 2 роки тому +1

    "because im not a magician" i wish she was my proffesor

  • @d7dh523
    @d7dh523 3 місяці тому

    Why did u use -3 for the second row unlike the first row ???

  • @SuperChelseaSW6
    @SuperChelseaSW6 Рік тому

    7:03 . how did u get -3R1+R2---->R2? why u putting -Ve before 3?

  • @waterfall-r1n
    @waterfall-r1n 6 місяців тому

    Hii love your videos which text book do you refer to?

  • @jennafaith1512
    @jennafaith1512 4 місяці тому

    Professor Brehm, what textbook are you using for this course? Can you post the info? Thanks.

  • @Curiosity_Carousel
    @Curiosity_Carousel 2 роки тому +8

    This 18 minute video is equal to = 2 weeks of lecture time 🤦🏽‍♂️

  • @davidmurphy563
    @davidmurphy563 Рік тому

    Paused at 2:21, let me see if I can do this.
    Ok, we need the inv matrix, so the inv determinant is 1 / 1*-2 - 1 * 3. So -1/5.
    So the new matrix is: {{-2, -3}, {-1, 1}} multiply that by the scalar and we get. {{2/5, 3/5}, {1/5, -1/5}}.
    Ok so now we multiply that by the output vector: {5, 10} * {{2/5, 3/5}, {1/5, -1/5}} = {{4}, {1}}
    Ok, let's hit play and see if that's what the lady got. Drum roll....

    • @davidmurphy563
      @davidmurphy563 Рік тому

      Yay, got it right! Woohoo! Wrote my notation weirdly - should have been {4, 1} but I'm calling that a win.
      The lady used some bizarre black magic to solve hers though.
      I'm not sure why she didn't just do an inverse transform? Obviously it worked though but all this advanced algebra is very confusing.

  • @davidxu2995
    @davidxu2995 Рік тому +2

    Which textbook are these videos modeling?

    • @Et3rna12un2h1ne
      @Et3rna12un2h1ne 8 місяців тому

      Linear Algebra and its Application by David C. Lay [4th edition]. Thank me later! 😊

  • @lordmiles9678
    @lordmiles9678 3 місяці тому +1

    explain!!!!!! where r u getting those numbers frooom!!!!!!!!

  • @bilalrehmat3714
    @bilalrehmat3714 3 роки тому +2

    Can you please help me which edition of Howard Enton you are teaching

    • @SawFinMath
      @SawFinMath  3 роки тому

      Now Howard Enton. First part of the video tells which Lay text I use

  • @sandeepkumarsurada8652
    @sandeepkumarsurada8652 3 місяці тому

    Could you pls make it clear for me that -3R1+R2=R2 and why only -3 ?????

  • @aribkamal3239
    @aribkamal3239 11 місяців тому

    Does anyone know what textbook i can follow for this playlist ? I have linear algebra next semester and I’d like to be prepared

  • @EVRIEONE1
    @EVRIEONE1 Рік тому +1

    I hope this series is better than others because LA is terribly taught or I just don't get this topic

  • @skybird7274
    @skybird7274 2 роки тому +1

    are you following DC lay?

  • @rgentil32
    @rgentil32 28 днів тому

    hi, what text are you using?

  • @PROSNORLAX
    @PROSNORLAX 5 років тому +5

    Hey professor, using your videos for class, thanks for all of this! @9:07 I think you forgot to multiply the four in the "b" column.

    • @SawFinMath
      @SawFinMath  3 роки тому +1

      Thanks for letting me know

    • @eevibessite
      @eevibessite 2 роки тому

      ua-cam.com/video/lOuKqOwsDgE/v-deo.html

  • @yz5128
    @yz5128 3 роки тому +1

    The way you write your row operations could be confusing for students who follow the definite on the book.
    "Replace one row by the sum of itself and a multiple of another row."

  • @binesh_iztleuov
    @binesh_iztleuov 5 місяців тому

    Which textbook are you using for this course?

  • @usernameusernameusername9835
    @usernameusernameusername9835 2 роки тому +2

    Hi ,
    Does your linear algebra playlist cover all topics that you would cover in a in-person course? Or is it missing some sections? Thank you very much!

    • @SawFinMath
      @SawFinMath  2 роки тому +1

      This playlist covers the course as I teach it now. But I will likely redo this course soon and may add additional sections.

    • @usernameusernameusername9835
      @usernameusernameusername9835 2 роки тому +1

      @@SawFinMath Thank you.

    • @eevibessite
      @eevibessite 2 роки тому

      ua-cam.com/video/0Ahj8SLDgig/v-deo.html

  • @kevinkasp
    @kevinkasp Рік тому

    Ms. Brehm, thank you for your videos/courses. I appreciate them so much. Would you tell me the Linear Algebra textbook you were using at the time? I’ll get it to read and supplement your lectures.
    Thank you again for everything.

    • @SawFinMath
      @SawFinMath  Рік тому +2

      Lays linear algebra and it’s applications. I think it’s 5e

    • @kevinkasp
      @kevinkasp Рік тому

      @@SawFinMath Thanks for that.

  • @GeorgeKevinRosas
    @GeorgeKevinRosas 7 місяців тому +1

    Could the practice problem still be solved with a matrix?

  • @debrito_ss
    @debrito_ss Рік тому

    what app do you use to show the equations ?

  • @itsmypersonalaccount
    @itsmypersonalaccount 6 місяців тому +1

    hmmmmm what has become of me, learning maths cause its fun. SIgh i know in the long run i have to use it in my game engine and development