Linear Algebra Final Review (Part 1) || Transformations, Matrix Inverse, Cramer's Rule, Determinants

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Studying for a Linear Algebra final? Stressed out? Don't worry because now I have a Linear Algebra Final Review video too!
In Part 1 we will be doing problems on Linear Transformations and making sure you understand what a Linear Transformation actually does, and what things like onto, one to one, and "in the image" or "the image of" mean. We will also do problems on the inverse of a matrix, if a matrix is invertible, finding determinants through cofactor expansion, upper triangular properties, and row reduction. Lastly, we will end with solving for a vector via Cramer's Rule.
I hope this video helped! If it did, please SUBSCRIBE for more content. Thanks for watching!
PLEASE consider supporting me on Patreon!!!!
/ ludus1

[@LudusYT]

Donations really help me get by. If you'd like to donate, I have links below!!! Venmo: @Ludus12 PayPal: paypal.me/ludus12 Patreon: patreon.com/ludus1

[@LumiRev]

Just going to comment the timestamps for everyone else! 2:41 Linear Transformations 17:05 Matrix of a Linear Transformation 31:00 Matrix Operations 36:55 Inverse of a Matrix 54:56 Invertible Matrix Theorem (IMT) 59:40 Finding Determinants 1:07:27 Properties of Determinants 1:16:30 Cramer's Rule

[@user-vn7ip5kp7j]

Thanks to you, I passed my linear algebra course despite failing both midterms. This was 2 years a go but I wanted to come by and say thank you a million times for assisting me pass the class. Without your help I would've failed. And even though youre not making videos your old ones still assist all of us.

[@becktronics]

Dude you are awesome, throughout the semester I despised linear algebra, but grew to love it with time. I had a super shaky foundation and after watching all three of your review videos I actually feel confident with the concepts... I feel like many people who try to teach linear algebra dance around the actual point of the ideas!! I hope I pass tomorrow. My class was brutal throughout, and despite high B's on 2 exams, getting an F on the first one left me barely clinging onto a C in the class.

[@LudusYT]

I completely agree with you! It doesn't help that a lot of professors have zero way to show you visuals in class (other than writing on the board), so maybe that is why so many tend to beat around the bush. Let me know how you do on the final! Feel free to dm me on instagram with your results. My tag is ludus12

[@muhammedsungursahin4837]

I love how high quality this is. Thanks man, this is gonna help for my midterms a lot.

[@stardustnation2480]

Man, this is a terrific resource! I have my final tomorrow and really appreciate this video and the content contained within. Very useful review, very concise but comprehensive.

[@user-xt8xh7tu9x]

BROTHER. YOUR METHOD IS SO CLEAN AND EASY. YOU ARE MY PROFESSOR NOW

[@DianaDiana-yl4yt]

I can do calc in my sleep but linear algebra? Not so much. These videos have made me feel a helluva lot better. Bless your smartypants soul! I might end up actually actually passing this exam.

[@benhorse681]

Bro all my finals are crammed in one single day. Just started to watch this video, if this helps I'm gonna send my love.

[@12356hy]

56:40 You can also do the determinants to check to see if it is invertible since det a ≠ 0 if its equals to zero that means its not invertible! :)

[@LudusYT]

Good point!

[@David-cx3fc]

This is saving my life for a job interview later this week! Took this class a few year ago, so this is a great refresher. Thanks for the awesome content, you explain things so well!

[@LudusYT]

Wohhh that’s crazy!!! I never thought my video could be used for that. That’s amazing! I’m so glad I can help you do that. Please keep me updated with how it’s going!

[@jaggysmf1860]

this man helped me pass calc 3 and is now going to help me pass linear algebra. i cant thank you enough. if i had the monies id donate some

[@y0da107]

you need more recognation man you deserve it for us !!!!!

[@LudusYT]

open circuit - Thanks! Hopefully the channel does start to do much better or we won’t hit 1,000 subs till September :/

[@Dina-he1uc]

Been a while since i took linear algebra and this is a good refresher! thank you so much!

[@dasliao]

OMG, This is the best, helps a lot. Final on tmr.

[@salenale1846]

Cramming this all in for my linear algebra final next Tuesday! Thank you for the videos :)

[@LudusYT]

Salena Le - Not a problem! Let me know if you have any questions at all. You can either leave them in a comment, or dm me at “learned_tutoring” on ig. If you know anyone else who could use these videos, be sure to let them know! Thanks.

[@hanauddin5904]

I’m going to share this with my class mates so you can get more views. Great work!

[@LudusYT]

Thank you so much!!! I’m glad I could help you.

[@bhavayashah5419]

I cannot thank you enough for these videos! My final is tomorrow and these videos have cleared up a lot of concepts! I'll be watching the Calculus 3 ones tomorrow (lol) Thank you again!

[@LudusYT]

Calc 3 and Linear Algebra at the same time?!?! Lol you must be a mad man. I'm glad the videos could help. Definitely let me know if you have any questions.

[@Armand__]

bruh linear algebra concepts seem harder than they actually are.

[@LudusYT]

I completely agree with that. I hope this video helped clear some of that stuff up!

[@Armand__]

@@LudusYT thx. It helped.

[@HDitzzDH]

The actual conceps are very intuitive, it’s just that the terminology, the way it’s taught and the symbols makes it seem very abstract and difficult.

[@notloc8993]

Love your content man. As one math major to another, it is really nice to see someone breaking complex topics in to more simple parts. You do a really good job at it and you explain your process well. If I could suggest, if you make another linear algebra study video, because of the school I am at known as the math school of my country they tend to teach more things that you would usually learn in second year in to first year. So In my Linear Algebra class, a lot of what you went over was covered, but I was wondering, if you do another Lin Algebra video, if you could cover linear operators, projections of complex numbers, determinants and eigenvalues with complex numbers, orthogonality and inner products, and proving things are linear like the property " f(x+y)=f(x)+f(y) and f(cx)= cf(x). Besides that man, really well done video and I cannot wait to see what future content you bring. Keep up the great work Ludus!

[@ryanjackson0x]

For #2, the reason that x is in two dimensions isn't that we're lacking a pivot, it's because the size of the input to a 3x2 matrix has to be 2 dimensions.

[@rohanjagdish5186]

great video thank you for making this! it helped a lot

[@wyatttempleton628]

if i pass this class because of you ill definitely be donating....

[@LudusYT]

Lol I'm sure you'll do great. Thanks for watching my vid, I hope it helped!

[@yagnapatel3912]

Thank you so much you are literally the best human being

[@p2p2p2p2p2p]

amazing review! you deserve more subscribers

[@mina_mozna]

Thank you so much for doing this.

[@justanother4009]

Great video very well explained very refreshing u go back into something that i didn’t understand but i said in my head how did u do that and u go back into detail

[@liesalllies]

Really appreciate this! My linear algebra final is in 3 days and this is such a great overview to refresh my memory. Really appreciate the neat handwriting and dark theme. Thank you!

[@LudusYT]

lies, all lies. - I’m glad I could help!! I do have the two other linear algebra final review videos that deal with some more challenging topics, so I hope those can help as well. Definitely let me know if you have any questions. Also, if you have some extra time, you should definitely check out my new video on Special Relativity. I’d really like to know what you think of it (if you’re into that sort of stuff). It’s the first video where I included visuals and animations, and it took a full week to make lol. Thanks again.

[@liesalllies]

@@LudusYT Oh I'm on the second video now and I just recommended you to one of my classmates. I'll check out your other stuff, too! What is your major?

[@LudusYT]

Lies, all lies - I appreciate that! I’m a physics major at UAlbany and I’ll be a junior this year. Btw, I’d be happy to continue this conversation on my ig (easier than YT comments). My at is “learned_tutoring”.

[@liesalllies]

@@LudusYT I dmed you

[@kendalwilliams5128]

Thank you so much! This is awesome

[@wardotard]

I subbed to help you reach 1000, and I'm very late to that party. Heh but I'll contribute towards the 30K mark. Thanks for the refresher man, Others do great as well, I'm not knocking anyone, but in terms of quality review I think you've done great. Appreciate you, and lets hope you'll bust out some diff eq soon! (Selfish request, I know.)

[@LudusYT]

Thank you!! Yea, I've got a lot of reviewing to do, but I should at least be able to get a few diffy q videos during winter break. I'll probably start from the very beginning and work my way through the course. I'm trying to think of the best way to go about making videos during winter break. I want to not only make a lot of independent requested videos, but also work on full courses that I'll sell on my website.

[@egotisticalfantasyfootball5482]

Thanks so much for making this man

[@iamkind29]

Absolutely brilliant explanations good job

[@LudusYT]

Thank you!!

[@daringdarius5686]

My new University didn't accept my Linear Algebra transfer credit so taking it again this summer... It feels very awkward and funny that I'm going to start my "refresher" to take the course with a "final" review, but I think this is the best way to prime myself and remember what I struggled with to work on that now (as the first month or so will likely be a breeze at it is just the core concepts)

[@AloneMaru]

Thank you so much for these videos! Thank you for showing examples and explaining the terminology. This class has been a nightmare lol! Will be watching the other 2 parts today since I have my final tomorrow!

[@LudusYT]

AloneMaru - No problem! I’m glad I could help. If you have any questions, feel free to dm me on ig at learned_tutoring Also, if you know anyone else that could benefit from any of these videos, be sure to pass them on! I appreciate it!

[@KitsisSportsAndFit]

howd you end up doing??

[@Troglodyte2021]

well done, man!

[@abdurrahmanyaman5700]

Keep going what you are doing !!!

[@LudusYT]

Abdurrahman Yaman - Will do! Thanks!

[@karanbedi5576]

you are a savior!!! thank youuuuu

[@williamanderson9525]

Great video man

[@sydneyguilfoyle465]

thank you for this video!

[@minhkiller2]

Final on Tuesday let's gooooooo

[@user-bu8mg7uq3s]

thank you so much

[@sebastianguerrero1251]

Awesome review! Quick question, how do you record your iPad screen? I'm also interested in making math videos and was wondering how to get started.

[@m35926]

Severely underrated channel. Thank you.

[@LudusYT]

The Passionly Passionate Nightman - No problem! Thanks for your support. Hopefully we’ll get to 1k subs soon, but I’m honestly just glad I can help. If u know anyone else that this video can help, definitely pass it on! Thanks again.

[@m35926]

@@LudusYT Will do. Just finished all of your Linear algebra review videos. Very, very helpful. Remember me when you have millions of subscribers!!!

[@LudusYT]

The Passionly Passionate Nightman - Will do!

[@berdanism]

very helpful video. thank you

[@LudusYT]

No problem!

[@skythanefx237]

41:57 ok, can someone tell me why i need to multiply by (-2) From where i know its (-2) Thanks

[@albinsopaj]

00:04:45 T tells you this: take any vector (or vector set-collection), defined in a space R^n, and tell me where to map it, and I'll map it if I'm given the transformation matrix.

[@LudusYT]

Thanks for that. I don't know why I couldn't say that because I feel like I knew that at the time lol. I'll probably remake the video when I do a linear algebra series on KZbin.

[@albinsopaj]

@@LudusYT @RichardFeynman once said: If you can't explain the idea to someone else in simpler terms, such that they understand it, then you don't understand the idea. We don't know what's going on in your mind. We only hear and understand what gets told by you. Regards.

[@LudusYT]

@@albinsopaj I appreciate you trying to apply that quote here, but I believe it is because I have a bad habit of zoning out, especially while speaking. I think that is more of what is going on here. While I don't disagree with the idea that I may not have completely understood T(x), I was able to correctly show how it acts similar to f(x). This leads me to believe it was a zoning out problem rather than a lack of understanding issue. I've thankfully been getting much better with this over the past year. Thank you for trying to help.

[@sohamkolhatkar3336]

Thanks man!

[@LudusYT]

Soham Kolhatkar - No problem. I’m glad I could help!

[@123bubbleup]

Thank dude!

[@Alekov_]

I found this by typing "linear algebra test". Never seen your channel before. Can tell you put a lot of work into this so I'll check your other stuff. You might want to work a bit on your SEOs to get some more audience.

[@LudusYT]

Alexander Kalis - Thanks so much! Trust me, I worked on keywords and SEO for a VERY long time, but I think it comes down to the CTR and the watch time on my videos. These two factors are what made people like the Organic Chemistry Tutor succeed and that’s why I’ve started trying to optimize for that. These final review videos haven’t done as well as I had hoped, but I’m have a couple videos in the works that I think can really do well. I’m most proud of the Special Relativity video I recently made. I think that could video could be my big break, but who knows? 😉 If you check out any other video, I definitely recommend that one! Again, thanks so much for your comment, and if you have any other tips, I’d be happy to hear them! You can DM me on Instagram if you’d like (easier than YT comments). My at is “learned_tutoring”.

[@shafqat1138]

You are a god amongst men.

[@serenashah9630]

night before da final xP

[@ChrisWhoLikesGrapes]

god bless you. simple as that...

[@KitsisSportsAndFit]

Great content dude!! I'm hoping that you're going to school to become a teacher, cause it really suits you. Really great job :)

[@LudusYT]

I'd ideally like to get an MBA and a PhD in Physics Education.. we'll see how that goes lol. Apparently that type of PhD is highly frowned upon in the Physics community. I really don't care about that though. Most of the professors I've had were terrible at teaching, so their opinions don't really matter lolol. I'm glad you're enjoying the channel, I'm so happy I can help! Let me know if you have any questions.

[@nimaseifi8723]

@@LudusYT I love this comment

[@oscarauza9401]

You'd be a hell of an engineer

[@user-fu2ni6dg9m]

ありがとう！！

[@ishandeshpande5269]

At 16:42 why did you assume that the -6 could be "zeroed out"

[@muhammadseyab9032]

In Q1. T: R^2 to R^3 or T: R^2 to R^2? ......

[@mohamed-obayalshaer5873]

dude I love u

[@bloodborneloverrr7646]

appreciate the black background. thanks

[@ifeanyiogbennaya7773]

What if i know everything u talked about in this video but still will fail a final exam? Does these videos cover every or most possible questions to appear on the exam?

[@LudusYT]

These videos cover nearly any topic that would appear on a linear algebra exam. I can’t see you feeling very comfortable with all these topics and coming anywhere to close to failing your exam.

[@cowboytv7903]

My first exam is in an hour and a half its all good tho i got Linear Algebra Final Review (Part 1) || Transformations, Matrix Inverse, Cramer's Rule, Determinants

[@mojow71]

If I get a at least a B on my final I will come back and donate

[@heeyoungabc8688]

i love you so much

[@LudusYT]

Lol, I'm glad I could help!!!

[@RaZorasiangamer]

Is this all of linear algebra? We did this during the first month or so of alg 2

[@samyud1819]

There’s two other parts after this

[@ryanjackson0x]

One-to-one: injective Onto: surjective Both: bijective

[@ryanjackson0x]

Might help if people are searching for additional information

[@opufy]

You're like our smart friend who wants to help us pass so we can all go to university together lol

[@Armand__]

final in 3 hours... wish me luck i guess

[@LudusYT]

Hope you did well on your finals! Got mine coming up pretty soon here!

[@joefuentes2977]

Linear Algebra is the only math that matters irl

[@MyVitros]

My final is today at 4

[@LudusYT]

Good luck!

[@nahleaky586]

t-12 hours til final exam...

[@LudusYT]

Hope you did great!!!

[@heeyoungabc8688]

thanks a lot

[@LudusYT]

No problem!!!

[@hacoba]

Good Schmitt

[@hacoba]

Graham-Schmidt *

[@LudusYT]

Jacob Abraham - Lol it’s gonna take a while to do part 2. I have to do a lot of reviewing myself on the more complicated topics so I think I can get the rest out by the end of next week.

[@hacoba]

Josh Martin haha no prob appreciate all this work you put in anyways

[@Unidentifying]

BOSS

[@nimethdesilva2820]

31:00

[@SexyDragonForever]

What is the point of it.. Like how do we use it in real life. I think thats why I am so confused because I can't figure out how it applies to the real world

[@LudusYT]

Harley Q - While I don’t know nearly everything you can do with linear algebra. I can say that it is extremely useful. Linear Algebra is used in Computer Science, Quantum Physics (I’m taking next semester), and it’s used in other classes as well. Linear Algebra is used A LOT in coding in the real world, and again I don’t know all of the other real-world applications. I don’t really think you should be thinking about Linear Algebra in terms of it’s real world applications - at least not while taking it in class. This is because you won’t find a one-to-one comparison (or at least if you did it would take forever) for each topic. That’s just like any other math class that you’re in though. The math that you learn is often just a tool that is used in Physics, Computer Science, Engineering, etc. If you want to think about what is ACTUALLY going on graphically when we do these different linear algebra things, I think 3Blue1Brown did an incredible series on this. While it’s not too academic, it will give you all the motivation you need. I hope this helped, and I hope this video helps you to study for your final! Let me know if you have any questions.

[@ryanjackson0x]

Just think of a matrix as a set of functions that act together. In that way, they are general mathematical tool.

[@andriejsupreme6759]

fuck i have my finals today, wish me luck

[@radiatedracer3830]

Don't forget to CYFA!

[@kwspp]

my prof really skipped most of the material and im sitting here lost as hell lmao thanks for helping tho

[@LudusYT]

Yikes... that's not good lol. Hopefully this video can clear some of that stuff up. I also recommend that you check out 3blue1brown's linear algebra series. That will dive deeper into the conceptual stuff.

[@hotdogjohnson]

Final in less that 8 hours, let’s see how I do 😳🙏🏻

[@ifeanyiogbennaya7773]

How did u do?

[@hotdogjohnson]

@@ifeanyiogbennaya7773 well I passed the class so that is a good thing AHAHA 😊

[@antoinecharlesdegaulle580]

@@hotdogjohnson Congrats! I have my final in 5 hours lol

[@mrwaffleman8732]

poggers

[@LudusYT]

POGGG

[@robertbrowne4431]

Less than 24 hrs till finals .. y'all think I stand a chance with these videos?😩

[@TheDuckTeamYT]

This is pretty good but it’s not good practice to say right in the video that you aren’t sure about the content that you are about to teach. That made me want to click off.

[@LudusYT]

I agree w/ you. I’ll remake this entire final review eventually and make it far better. I made this the semester after taking linear algebra bc I knew students like me could’ve used a KZbin video for final review.

[@gregoryG540]

thanks for trying, but you aren't good at actually explaining what these terms mean like, you don't present anything well at at. Just a few things I noticed I think you could improve at. You did pretty well trying to connect different ideas. I stopped watching at 25 minutes

[@LudusYT]

Gregory Gross - I’m sorry to hear that this video didn’t help you. Could you please give me examples of a term that I didn’t explain well, or times that I did not “present anything well at all”?

[@LudusYT]

Gregory Gross - And also, if you have any questions, let me know. I will do my best to answer them over chat.

[@davidelfvinglong]

This is a final "review", nobody should start this video expecting the creator to go over everything in depth. Don't even bother replying to comments that don't give you constructive criticism. Thanks for the video, I definately got alot out of it.

[@LudusYT]

David - Thanks for your comment, and I’m glad I could help! I wasn’t sure what to think of Gregory’s comment when I first saw it.. I wasn’t sure if he was trying to be constructive at first, but the “you don’t present anything well at all” really through me off. I definitely agree with your main point though. I can’t teach an entire course in one video. I even stretched this final review out to three videos (sorry abt that) just so I could cover everything in decent depth. That being said, I know I’m far from a perfect teacher. If there is anything I can do better, I’d be happy to hear anyone’s input as long as it is constructive/respectful. Maybe Gregory was trying to come off that way, I just didn’t perceive it that way. Again, thanks so much for your comment!

[@sameersharma7449]

@@LudusYT You gon go places man, I have my final in a day and this really helps as revision. In fact, a lot of conceptual understanding was revised as well. Thanks for the video, it really helps. Ignore the dude, you will get hate comments regardless of what you do. Thank you again for the review videos!