Linear Algebra 6.5.1 Least Squares Problems

[@thezeneris]

I'm a 44 year old stay-at-home dad and a college junior. Your Linear Algebra and Discrete Math playlists have been a lifesaver. Thank you for all the good work you do and thank you for sharing it with us!

[@wrestlingscience]

Are you studying computer science?

[@thezeneris]

@@wrestlingscience I am a Data Science major.

[@muhammadabdullahriazbhatti]

@@thezeneris How's it going so far?

[@thezeneris]

@@muhammadabdullahriazbhatti I only need 2 classes in the fall to finally get a degree. I've also had an internship and am looking forward to going back to work with my new skills. Thanks for asking and how are you?

[@thezeneris]

@Akash S For my degree, we were required to study differential and integral calculus as well as multivariable calculus. Then there was linear algebra followed by advanced linear algebra with optimization. We also studied one semester of discrete math, probability and statistics, statistical inference, regression analysis and finally statistical and machine learning. There is also a fair amount of programming in computer science classes and data science classes and while they were not math classes, there was often math involved.

[@aukusitinoah-yek99]

Thank you so much for doing this series! You really do deserve more credit. These videos have allowed me learn Linear Algebra throughout this quarantine!

[@SawFinMath]

Glad I could help!

[@pietropecora1335]

coming in clutch hours before my final, i've been using your videos since youre discrete math videos. thank you!

[@SawFinMath]

Thanks for watching! Glad I could help!

[@jacksatcher8010]

Thank you so much for these videos. You have been a huge help to 31,000 people so far with many more to come. Youve certainly been one of the only reasons my grade and understanding of this course is where it is now and I can't thank you enough making this free for everyone.

[@jakubkuczynski4115]

True

[@Damdahlf]

I usually don't leave comments on youtube videos, but I just wanted to thank you for these amazing videos. I was not a fan of how my college professor was teaching Linear Algebra, and my grades were suffering as a result. I quickly turned to youtube for help. Upon finding this playlist, I began skipping lecture and watching your videos instead. Let's just say I made the correct decision. I am currently sitting at a 93% in the class with only a final quiz, homework, and exam to go! Thank you so much!

[@SawFinMath]

Thanks so much for the kind words! Glad I could help!

[@wrestlingscience]

You are the linear algebra youtube goat. You use simple language, pre-pare slides so we dont just sit there watching you write stuff, you show all work and speak clearly and explain reasoning without becoming too theoretical and abstract. Everything i wrote is what my professor does and makes learning from his videos so difficult. Thank you for teaching this way and for helping me

[@SawFinMath]

Happy I could help!

[@throatgoat69420]

Hey I dont think I've ever commented on a youtube video but I feel like you really deserve it, I'm in college taking linear algebra and the lectures/textbook just over complicate everything. After watching your whole linear algebra series, I have never felt more confident taking the final today. Thank you for everything!

[@brilliantstarss]

I just can't say how grateful I am, Kimberly! I loved your course from the beginning to the end. I loved your teaching and your subtle humor. It was such an amazing time. Thank you very much for this. I hope you can reach more people! You are the best! Keep on being amazing! Now, I'm going to your calculus and I am already confident that I will get so much knowledge!!!! Thank you so much! Stay blessed!

[@pianodan1608]

You did linear algebra before calculus ?!

[@nickyggoodman]

Thank you! I have been coming to these videos whenever I have a hard time wrapping my head around what the book is saying. It's nice to have a replay of what we went over in lecture. Much help during my review :)).

[@bloodyglitch1777]

Watched every video in the playlist for my summer linear algebra class. The prerecorded college lectures were in 240p with a bad microphone. Thanks so much, you saved my butt in this class (and discrete math)

[@denaude7058]

Thank you, Prof Brehm for explaining Linear Algebra so well. I've watched so many other youtubers, but you were the one that got through to me. Greetings from South Africa.

[@king069-xr3hm]

Thanks Kimberly! You are a great teacher I consider myself lucky to have found your KZbin channel.

[@ricardotrevizo7059]

You saved my college GPA! I'm definitely gonna show this playlist to all of my friends who are going to be doing linear algebra, thank you so much!

[@yusufduman8737]

I don't know if she is the biggest but she is very big. Thank you Kimberly Brehm, thank you so much..

[@ahmadabdullah262]

Thanks for the course. I recently just learned about the linear regression algorithm and its basically what you've been teaching in this last unit. Taking a vector and trying to split it in two orthogonal vectors

[@kaijohnson3553]

Truly truly thank you Ms. Brehm for this playlist. You are such a great teacher. Hoping I do well on my final tomorrow!!

[@jasperjansen1150]

I am a senior in college and needed to pass this course to set me up for a class in my final semester. Wasn't feeling confident in my abilities to score highly enough to get a good grade to earn credit. I watched all your videos and worked all the problems as you went through them within a 2 day period as I crammed for the final. I ended up not only passing the course but getting my highest exam score of the semester on the final. All thanks to you! Great series!

[@SawFinMath]

Awesome work!

[@kassymchurchman5511]

this cousre in addition with series of vids “essence of linear algerbra” is really a key

[@angelasmith7894]

For the last practice problem at 16:35, I got a slightly different answer for step 4. I got -5 instead of 5. I'd show my row operations but it doesn't seem I'm able to put in a pic in comments and writing it out like I did below is too cumbersome. Hope this helps others. RREF: 1 0 0 1 3 0 1 0 -1 -5 0 0 1 -1 -2 0 0 0 0 0

[@SawFinMath]

Yes it should be -5. It's an error. Thank you for letting me know!

[@gillianmarlow404]

Just passed my linear class with a very high A because of your videos. Thank you so much for what you do!

[@Sikoro_]

Dr. Brehm, THANK YOU so much for this video series! When I started this semester with the pandemic going on, I had no clue of what was going on in Linear Algebra since my professor made his lectures confusing and much more difficult than they needed to be. Fortunately my lectures followed the same six chapters that you covered in your course, so I was able to follow alongside with you! After studying and working hard on my HW, exams, and quizzes, taking notes from your videos, and going back when I got stuck, I'm happy to say I got an A in the course :) Again, thank you for posting this video series and I hope you continue to help many people by posting more math videos!

[@SawFinMath]

Thanks so much for taking the time to write this. So glad I was able to help!

[@ahmedobn8866]

Words cannot describe how much I thank you. God bless you❤️

[@saraf4782]

Thank you so much for making this series! Using it as a crash course before my exam!!

[@jovantay521]

These videos are amazing. We happen to be using the same textbook for our linear algebra course and your videos breakdown the concepts so well. tysm!

[@jayjani5427]

You are actually amazing!! Thanks for all of your videos and help!!

[@Asterics.]

Thank you ms. brehm, I finished the course in 16 days, definitely need some recall to all of those. Anyway this course is so helpful for me, I finished an entire course even before the semester is even started yet.

[@thumsdown1]

I am starting my part-time school. My teachers recommended your channel to re-visit the basics of maths. Surely, I learned a lot more in a simpler way. Thank you for this series.

[@SawFinMath]

That's fantastic! Where are you studying?

[@thumsdown1]

I would be studying Advanced studies of Wireless Embedded Systems.Digital Signal Processing. I have been working for 8 years. So kind of needed revisiting maths for graduation studies. Surely, the way you give a problem to solve and then go ahead with solution really feels like taking in-person tuition. Thank-you once again.

[@thumsdown1]

@@SawFinMath ucsd

[@shengtong6772]

Report an error: at 16:19, the last element in the second row should be -5 rather than 5. Anyway, it's great!

[@daniyelzhumankulov7733]

The same thing. I redid it because of that. Confirm that it should be negative 5

[@SawFinMath]

Thanks for letting me know! Yes it should be -5.

[@Ryan-cx4ni]

Thank you so much for making these videos. You helped me pass my linear algebra course!!

[@gabrielmena2723]

Thank you so much for this series! You have no idea how helpful you've been for many students taking linear algebra, I'm projected to pass this course with an A thanks to you!

[@SawFinMath]

Awesome!

[@angelasmith7894]

I love your videos! Just want to mention a minor error in your matrix transformation at the 6:00 min mark. In the first transformation you show that the 3rd row reduces to [0, -1, 0] when it should be [0, 1, 0]. The system is still inconsistent so the outcome is the same. 1 1 2 1 1 2 0 1 1 ~ 0 1 1 1 2 2 0 1 0 Thank you so much for your videos!

[@SawFinMath]

Thanks for letting me know!

[@maryambibi2183]

THANK YOU SO MUCH FOR THESE VIDEOS.....trust me I learned a lot of things in linear algebra. I do have linear algebra course in my 3rd semester and was struggling with it. Thank god i got your videos. You deserve more than any likes or comments.... LOTS OF LOVE FROM A STUDENT ..

[@Megajim454]

Thank you for all your clear explanations throughout this series!

[@confused6526]

Thank you Prof Brehm. What a great journey!

[@buh357]

Thank you so much for your time and effort. I am learning a lot from you. I wish all the best for you and your family.❤

[@SquidyMeg]

Thank you for this I know im 4 years late but im still thankful

[@Spatzable55]

Thank you for taking the time to make these helpful videos!

[@DoggletPug]

Thanks for all your hard work Prof!

[@muhammadfardeen9194]

First of all iam going to say that i watched this whole playlist in 5 days before my linear algebra final exam and you taught that much accurate that i knew how to solve tha whole paper may Allah bless you sister ❤

[@SawFinMath]

I love comments like this! So happy to help!

[@nahtaly5255]

Thank you so much! You make wonderful content that is easy to understand.

[@youreyesarebleeding1368]

Well, my final exam is in 6 hours. Thanks to this series, I will have officially passed Linear Algebra

[@SawFinMath]

Awesome!

[@SliverHell]

thank you. i really appreciate all of your lessons

[@SawFinMath]

Thanks for watching!

[@warhammer48]

Thank you for doing this series it helped me a lot! If you ever go back to do this please add 5.5, 2.8., 2.9, 4.5(Especially 5.5) . That would help future students a ton! Again thank you for doing this.

[@SawFinMath]

I may be redoing this series with a different textbook soon (Larson)

[@WOLF91]

Thank you, your videos have been incredibly helpful.

[@SawFinMath]

You're very welcome!

[@ranarafay6880]

Watched complete playlist, that as very helpful. Thanks for this incredible content. :)

[@nikolinasilfverberg6692]

Thank you so much! You made me understand linear algebra!

[@zuko803]

finally I'm finished this class but I will find the rest of chapter which is chapter 7 in the other channel, I want to say thank you so much, its really help me understand math in machine learning model that I want to learn, thank you maam!

[@nessessence8261]

just complete the series, appreciate!

[@SawFinMath]

Great work!

[@Casual314aA]

You are AWESOME. Thank you so much.

[@SawFinMath]

Happy to help!

[@manjunathreddy777]

i had an exam tommorow u explained well that iam getting confident abt this topic

[@mokoepa]

And today I made it to the last video in the playlist...

[@ceejay1353]

So Just want to be clear, is this course at this point enough to have a foundaila understanding to move onto other Compsci /Math Courses that need it?

[@Sayantikadas12]

Don't we need to find the b(cap) and hence the error in the last practice question? Kindly explain this ma'am.

[@tunabirdy3567]

Thanks for the class. However, this last example should not have free variable since A has independent column vectors so that At * A should be inversible.

[@kikimobolaji5368]

Thank you for your vidoes. I got 100% on my matrix final :)

[@gerardtyson2274]

Are the following topics not covered in this course? Cramer’s Rule Markov Matrix Complex and Hermitian Matrix Positive Definite / Semidefinite Matrix Markov Matrix Singular Value Decomposition Change of Basis

[@SawFinMath]

Correct. We don’t cover those topics.

[@gerardtyson2274]

@@SawFinMath perhaps you could make a Linear Algebra II course playlist covering those topics

[@SawFinMath]

I am considering a refreshed playlist for this course that would cover more topics.

[@larshaji6117]

best teacher I have seen ever, Thanks

[@SawFinMath]

I appreciate it!

[@MichaelBomett]

Much appreciated, very helpful 👍

[@johnk8174]

nice complement to Strang; thanks.

[@SawFinMath]

Thanks! I haven't used the Strang text, but most Discrete texts cover 80% of the same material with variations based on the focus of the course.

[@johnk8174]

@@SawFinMath I meant Gilbert Strang as the internet popularizer of linear algebra more than as the textbook author (though his books are wonderful too); I don't know how many millions of views he has for his linear algebra videos on KZbin, but good portion of them were from me :-). I meant great praise by comparing you to him.

[@SawFinMath]

Well thank you so much! I will have to check out his videos!

[@confused6526]

Prof Brehm.. Throughout the lectures you kept saying "check...check but I only see that you did one "check" using the Nike symbol 😃 Then .. in this lecture I realized why you kept saying "check..check". By that you you meant one check down (\) and then another check up (/). So the final of "check.. check" = \/. 😃

[@boggavarapunikhil2745]

Thank you so much for great explanations.

[@SawFinMath]

You are welcome!

[@lgl_137noname6]

Professor Brehm, Thank You so very much for your presentation of this material. Very effective. Will there be follow up courses with presentations of SVD ? Please advise, Regards GL

[@SawFinMath]

Thanks for watching. I have no plans at this time for SVD. I teach undergraduate mathematics and that topic is not in our topic list

[@davidusmonov5148]

Great explanations 👍👍👍

[@SawFinMath]

Thanks!

[@angelasmith7894]

For the last problem wouldn't we still need to calculate b hat and the error? Those were steps 4 and 5 in the second to the last problem, but not in this problem..

[@SawFinMath]

Since we weren't asked for the error, I didn't complete that step.

[@ahmedmusa517]

Hello, can I calculate b-hat by projecting b on A ? then I can easily calculate x-hat by taking Ax=b-hat

[@SawFinMath]

I don't believe so, but you can give it a shot and let me know how it turns out!

[@ahmedmusa517]

@@SawFinMath Hiii it did work I got the same result ! but I had to use Gram-schmidt process first because the basis of subspace are not orthogonal. It is vert easy method coz I did not calculate the AT A and AT B ....etc

[@VALOGAMERPK]

thanks professor Brehm

[@einayis]

hi Madam Brehm! is the video 6.4 and 4.4 missing?

[@SawFinMath]

I don't cover all sections in the textbook

[@einayis]

@@SawFinMath I see 😊

[@mohammadhamzaali6619]

the RREF for this is actually 1 0 0 1 3 0 1 0 -1 -5 0 0 1 -1 -2 0 0 0 0 0 slight mistake but awesome video overall!

[@batuskovichuman6886]

this is it guys.

[@muhammadabdullahriazbhatti]

did you skip gram schmidt process for 6.4?

[@SawFinMath]

Yes. We don’t cover that in my class so I didn’t make a video for it.

[@muhammadabdullahriazbhatti]

@@SawFinMath You probably skipped Singular Value decomposition from chapter 7, also. Is that right?

[@njoy2075]

why in Step 4 we can not use the generic formula b^=Sum((b.u/u.u).u) ??

[@SawFinMath]

Does it give you the same result?

[@angelmoronta3771]

thank youuuu!!!!!!!!!!!!!!!!!

[@lsjmartin6220]

This is The END...

[@tamsaasoo5418]

GOAT

[@amon6743]

Thank you very much

[@cameronsantiago3155]

And we are done!

[@ivanminchev888]

tysm

[@davidusmonov5148]

Wow, great videos. Thanks a lot. Can you give your brain just for one day?🙃 I need to pass my exams. Anyway I trying to copy your brain

[@SawFinMath]

You don't need it! I bet you did great on your own!