Gaussian Elimination & Row Echelon Form

[@TheOrganicChemistryTutor]

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Thank you 🙏

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Your videos are so much easier to understand than my lectures. Thank you for carrying me through university xD

[@amreenaym786]

Y’all are learning this in uni? Bro I’m having a hard time understanding this and I’m a freshman in hs

[@higgsboson6274]

@@amreenaym786 just keep going, keep practicing. things will make sense eventually

[@suraboss2673]

@@amreenaym786 its literally going to be easy learning this in university

[@josiahscarrmusic6750]

@@amreenaym786 you do repeat stuff to regain that familiarity, though I am learning this cause I have a maths module as part of my CS degree

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@@amreenaym786 in my country we don't learn this stuff in high-school, so I'm learning this for the first time in university

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This man carried me through 1st year and now hes carrying me through honours as well. You are a true legend!

[@aimokoivunen4787]

Best of luck!

[@master_baiter1873]

His exapmles are ass though. He picks the easiest examples. He could give a harder one.

[@droomahbroo9291]

@@master_baiter1873 well he’s not going to do ypur homework for you :D. I usually watch the video to learn the basic concepts and then go through the examples and exercises given in class. I then use his examples to boost my confidence the morning of the test. Seems stupid but its gotten me through Physics 5 so…

[@master_baiter1873]

@@droomahbroo9291 i mean he could give one hard example. He chose easy examples. Ones i can easily do in my head.

[@GoToMan]

@@master_baiter1873 I suggest you pick up Strang's linear algebra

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This guy explains it so well...my textbook explains it like a brick.

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For real though

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@@zinkeyminaze7018 He's got the voice of an angel sent from the math gods

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Textbook is pretty much a piece of brick

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Really, where r uh from

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I have an exam tomorrow,and I’ve been trying to learn this from scripts of my teacher for 3 hours and there is a guy like you that teach me all the stuff for 18 minutes.I wish you a good health and life.Thank you

[@taekwondotime]

This seems to be a common misunderstanding with matrices. *Echelon form is simply the final matrix after you've finished Gauss elimination* . (The matrix at 6:10.) It need only have 0's in the lower left-hand corner. *There is no requirement to have 1's along the main diagonal because they do not help in solving the problem* . They are simply wasted operations and are not done in practice. (Unless you want to do Gauss-Jordan elimination... which is also not used in practice.) People seem to confuse the two. You only need 1's on the main diagonal if you're prepping for Gauss-Jordan elimination which then transforms the numbers in the upper right corner of the matrix to 0's as well. If you're not doing Gauss-Jordan, then don't worry about having 1's. *Once you obtain the matrix @**6:10**, then we know that 4z = 8 and therefore z = 8/4 = 2* . From there we use back substitution to solve for the remaining variables. FYI: This is straight out of my math textbook if you don't believe me. *Source: Advanced Engineering Mathematics by Erwin Kreyszig*

[@taekwondotime]

TIP: The *scale* operation is your friend! As soon as you start getting into non-trivial matrices where the coefficients don't eliminate nicely, use the scale operation to get them up to a common value and then eliminate them. This helps you avoid ugly fractions and awful decimal numbers that have infinite precision. For example, consider the following system of equations: x + y - z = 9 8y + 6z = -6 -2x + 4y - 6z = 40 Without using the scale operation, you'll hit a wall by about step 3.

[@pablonapan4698]

Thanks

[@dami4271]

@@taekwondotime so whats the scale operation

[@WTHnada]

You should have explained that in the video I was so confused :(

[@alsudairy.k5647]

The one he did is called Reduced Row Echelon form.

[@hybe8459]

يبني والله ال انت بتعمله ده عظمه فشخ ربنا يخليك لينا كلنا بنحبك والله كل ال في هندسة حلوان المطرية بيحبوك والله و بيشكروك على مجهودك معانا انت راجل محترم و ربنا هيكرمك و هيخلي عيالك يبقوا احسن ناس في الدنيا حبيبي يا دوك

[@martinvich5796]

couldnt agree more. xddd

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This youtube channel is literally my first year of my BSc's saving grace. I can't thank you enough.

[@HappyCrayons-eu1fy]

Thank you Jesus my redeemer for revealing this to me after hours or practicing! Guys, you have to use the columns. Literally go from row 1 column 1 and make this value =0 (or interchange rows if necessary), then go down in column 1 and use a relationship with respect to row 1 to get a value. Continue until all values below the initial '1' are =0, then move to column 2 and establish a diagonal (similar to an identity matrix below the diagonal, but with the updated values above the '1' diagonal.) I trust this hopes, keep practising and you WILL get it. Live excellently and don't give up hope!

[@mosessydneyruiz87]

I am here because of the online class. Self-study huhu. Like also if this is your case! Goodluck to all of us!

[@Rob-J-BJJ]

haha yeah im taking linear algebra online

[@annedeborah5926]

Same reason 😅 All the best to you too!!!

[@RealSupaHotFireVEVO]

@@Rob-J-BJJ Same here lmao.

[@americanconsumer4496]

Same!!!!!! Tough stuff

[@Anand-zt3wv]

Where we at gang?!!!!!!!!!!

[@paulvanbrakel]

For the people that get confused at 10:50: 'R3 = R1-R3 is the same as 'R3 = -R3 + R1. He writes it in a different way, but you're still working on 3R in both cases

[@parthbhanushali9382]

thanks a ton mate

[@muhammedowais8541]

Thanks man now i think i understand.

[@sreekumarnair-rl2wo]

I don't understand it why it's R3=-R3+R1 we can directly go with R3=R3-R1 isn't it? Please help me with this

[@oimatesimro2088]

@@sreekumarnair-rl2wo i think its because you have to write the ending row (R3) at the end of your operation, he explained it in another matrix vid, i think its the row operation vid

[@ckaamuli8182]

@@oimatesimro2088 wouldn't R3 = -R1+R3 work then?

[@ddahstan6876]

One of the most humble educators that we're blessed with! A heartfelt Respect to your dedication and patience because a lot of us will survive much longer in math, or even feeling more motivated!! 🍭

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I am in maths major and this year is my second year in this department. Before online education, I was learning with your videos. Actually my college is very hard but you solve easy question,so I love your videos, because I feel like I am a paradox in class of my teachers. It is very awful situation. I am so glad to discover this channel thanks the organic chemistry tutor

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have u graduated already?

[@BigBrother4Life]

They always do the easiest question on the internet.

[@TheGunzSkido]

well you only need the basic anyways for this kind of question.

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[@TheGunzSkido]

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Otherwise we could be afraid of how difficult it may be : )

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[@jackdeily8615]

My brain does not let me do this. I have been trying so hard for a week and I feel like my head is going to explode.

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Same here brother :(

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Currently stuck myself.

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same

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same

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I just wanna say, you've helped me so much over the past year. Precalc, calc 1, a calc 2 crash course over the summer, and now linear algebra. I doubt i'd of been able to understand everything as much as I do now without your videos helping us walk through each new method and idea. Thank you for taking the time you have to help us learn

[@MARIN-py9ye]

My prof. explained this to me 3 times and I didn't get it, watched your video one time and figured it out instantly. Perfect job on the tutorial, thank you!!!

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[@aimokoivunen4787]

Felt so lost after my professor taught this. Came here for help as always. Was not disappointed. You're a good man. Thankyou

[@ez5267]

We have an exam tomorrow, including this topic. Hoping to pass it.

[@neilialopez7446]

I have one tomorrow too cri.

[@ahmetkarakartal9563]

@@neilialopez7446 ahahaha me too

[@tarylee357]

updates? how was it! im having one soon :)

[@PenandPaperScience]

Hope it went well. And for those students out there that want some more practice on Gaussian Elimination, I've made a video where I solve such exercises step-by-step. It might help some :) kzbin.info/www/bejne/pKq6oWypp52ofac

[@StevesUniverse]

UPDATE??

[@dania8183]

A THANK YOU COMMENT IS NEVER ENOUGH TO YOU GUYS!!!! LIFE SAVERS!!! THANK YOU VERY MUCH TEACHER, THE ORGANIC CHEMISTRY TUTOR.

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[@georgesadler7830]

MR. Organic Chemistry Tutor, this is an excellent introduction to the Gaussian Elimination Method and Row Echelon Form in classical Linear Algebra. Linear Algebra is very useful in different levels of mathematics.

[@merkly5858]

Words can not describe the way this man has helped me get through all of my studies. At this point i don't even know why i go to lectures when i know that this channel has got my back.

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[@timothylittlefield]

You corrected both z=2 and -2 in the top row. Great job and thank you! I can solve variables using Gaussian elimination.

[@dazzlingforests1373]

Thank you for writing that he caught that! I was getting worried lol

[@joanhewitt-fagan2815]

thanks. you are absolutely the best, my math teacher totally confused the class with this principle.

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[@nightfox1416]

Great video! Only advice would be explain what you can do to simplify the matrix into row echelon form. For anyone watching, these are 1) You can swap the rows (you CANNOT swap the columns) 2) You can multiply the rows by any constant (in a similar way you would when solving simultaneous equations normally) except zero 3) you can add or subtract one row from the other (you see this often in this video)

[@inarvii8181]

I am a bit confused as to why in the second example, he did R1-R3. Why would it not be R3-R1 so that it is 2-2?

[@sonu1747]

@@inarvii8181 correct

[@thedrumminggamer1064]

your videos are 10x more informative than any lecture i have sat , keep up the good work

[@timbarrett4580]

I literally didn't understand how this worked and my professor never really did any problems out. Watching you solve it made it seem so trivial. Thank you so much!! You are amazing

[@rashidissa5887]

Jack, me longer than a week, but have not lost hope. Never did matrix in my O-Level I am gradually catching up. Imagine in my late 70's, but still pursuing maths. I love it

[@shereeannrichards3901]

You made this so easy to understand and follow. For days I have been losing my sanity trying to complete my assignment on this topic. Thank you

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same

[@youssefbayoumi2694]

can i minus 2 rows ?? someone answer plz

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Love how he explains everything in such a short time and detailed

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the solution is INCORRECT!!!!!!!!!!!!!!!!!!

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Thank you so much for the explanation! I can't understand this in my textbook and all and you only took 20 minutes for me to completely understand this concept!

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I had a hard time solving this but thanks to you it’s much easier 🎉

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Oh man, this just smacked me in the face, in a good way. Great breakdown. I am embarrassed to admit how much time I wasted with other resources before coming to this channel. I won't make that mistake again. Thanks for the insight!!

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Simple, clear, and self-evident. Many thanks!

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You made this so much easier ! Thank you!

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First day of college and already here, thank you as always ❤😂

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Doing the lords work with this video, awesome explanation!

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Slay king I understood it because of you😍😍😍😍

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He has been my saving grace in 5 different classes so far

[@mr.creepz]

thanks bro you made me understand this topic in just 20 mins while my teacher was teaching it from 2 months

[@diachyti]

How did i understand it so easily i have been trying to read about this for hours no good, what 16 mins and now and am pumped up to do some math

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I am about to owe this man my whole degree

[@jinxinchan7981]

Thanks. I am taking this class online this summer term. Reading the material for 19 times, I still doesn't understand. Now... there is hope :)

[@LS19981]

Hours of reading about Gaussian elimination doesn't measure up to the first 2 minutes and 28 seconds of this video. Thank you.

[@bfremming]

Wait! - at 7:48, why is [1 | 2 ], converted to 1x = 2. Shouldn't it be 1z = 2?

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I'm literally skipping classes and learning from him

[@apheniesinegal2287]

I love this KZbin channel it helps and explains better than my professor

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Get more on Gaussian elimination method of solving systems of equations from this link kzbin.info/www/bejne/m4mrgKyqnryKd9k

[@user-pf4cj7kb5e]

7:40 the solution of the first row in the upper left corner is -2, but on the upper right corner its 2. I think you had a typo EDIT; oop you corrected it. Nevermind alls great ^^

[@xpencer9563]

6:49 all 1st row will retain, should be "-2" 7:35 x+y-z=-2 Nvm. You've already correct it. ✌️

[@safasediq9777]

16:13 If you can get the answer without putting it fully in Row Echelon form (with the 3 0s thing you did at the end of the video), why would you ever need to put it fully into row echelon? Wouldn't be easier to get the 3 zeros rather than changing it fully? If I am wrong, please let me know when i would have to put it in the full row echelon form/ when i can't get away with making three 0s? Not sure if i articulated this very well, sorry!!!

[@Mahin-yp4uz]

same question i have

[@MikeGowaseb]

thank you very much, time to cook my test

[@K_K1010]

Can I apply changes to row 3 by R3-R1 instead of R1-R3 in10:58? Cuz I can still get a 0 at the bottom left corner.🤔🙏🏼

[@sreekumarnair-rl2wo]

I also have same doubt. It's R3=R3-R1 right? Then why to take R1-R3 cuz R3 left corner we wanna make zero, right? I did by R3-R1 but my answer compared to him is wrong😢

[@MoiraBrady]

Thank you. You explained it so well and now I can practice this till I can do it without help. Really helpful and you have taken the stress out of my weekend :)

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I don’t even need to know this yet I scan understand it so well. Your goated.

[@safiullahshah8550]

Wish I could pay my tuition to this guy instead of my college

[@solomonpersaud7126]

isnt subtracting row R1 by R3 gonna change R1 since you're subtracting/- by R3 ? clarify @11:11

[@Viridian88]

Do not be confused. You're writing a new matrix by using R1 as a "model" and basically rewriting R2 as a linear combination of R1+R2 (multiplied by the most suitable numbers), but you're actually keeping the "model" row untouched. Why? Because your aim here is making the "x" coeffficient (that is to say, the numbers that are BELOW the first number of the first row) equal to zero - EXCEPT for the first row, otherwise you'd nullify the informations given by your system. Same goes for R2 when you're using it as a "model".

[@noelkuhomiemaihi5542]

My favourite online tutor.Just a little correction here l think you mean to say z=2

[@devOmarAZ]

From Egypt>>>> Thanks ..... Your The Best : )

[@ryankeshet5820]

Why are you so helpful all the time?

[@computersciencewithpeter]

Love how you exemplified all the concepts...

[@pfeliciano4062]

How do you know which rows to use to get a o? Is there a specific order? How do you decide on R1+R2 or R1+R3 in a case where you could use both to get a 0. Also How did you know which number to convert into a 0 at first on 11:35?

[@sookiriashan3101]

There isnt specific order, you can select any row with another which make (1,2),(1,3),(2,3) elements on zero state :)

[@emilytran212]

I learned that there isn't any specific order. As long as your strategy is to eliminate/ cancel out variables in a 90 degree angle fashion like how he explained on 10:13, then you are good because if you think about it, that 90 degree angle method will allow you to solve your first variable (do so with the equation that has 2 0's next to each other). Then, you can plug that solution into your other equation with a 0 variable and so on. It does not matter which part of the matrix you decide to place your 90 degree angle.

[@Viridian88]

You'll definitely have to use: the very row you're gonna rewrite and the "leading row" that you'll leave untouched. For instance, if you want the x-coefficient to ONLY appear in the first row, you'll consider R1 as the leading row... and then, you will rewrite R2 as a linear combination of R1+R2 (multiplying those rows by an appropriate scalar).

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missed you man for 2 years at CS

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Passed my math exam coz of you. Thanks a ton :))

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Give this mister a Balon d'or😭😭😭

[@pleasemebelieveme2679]

This topic almost caught me of guard but where I come from my teachers call it simultaneous equations that we convert into matrix. I guess u learn smth new every day

[@slimycat_bedrock]

I learned this back in Middle School, but I forgot this was of doing it. Thanks.

[@normanhenderson7300]

I have not yet been acquainted with a video on this subject as yet that teach this method in a clear and systematic way. This one included.

[@hoyter_toyter8793]

Why is he better than all of my professors?