Gaussian Elimination & Row Echelon Form

[@TheOrganicChemistryTutor]

Final Exams and Video Playlists: www.video-tutor.net/ Full-Length Videos & Worksheets: www.patreon.com/MathScienceTutor/collections Next Video: kzbin.info/www/bejne/m4q2coaubcShr8k

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Thank you 🙏

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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!

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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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Textbook is pretty much a piece of brick

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[@youssefbayoumi2694]

can i minus 2 rows ?? someone answer plz

[@PenandPaperScience]

@@youssefbayoumi2694 What exactly do you mean? You can indeed add a row with minus 2 times another row.

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[@mrguys2822]

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

[@oluwakoredeonasanya3267]

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

[@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]

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[@martinvich5796]

couldnt agree more. xddd

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What I wonder is that his title is chemistry tutor😂😂😂. But teaching math more than math teachers😅😅😅😅

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

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haha yeah im taking linear algebra online

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

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@@Rob-J-BJJ Same here lmao.

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Same!!!!!! Tough stuff

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[@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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[@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??

[@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

[@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?

[@aimokoivunen4787]

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

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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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bro its like if the devil tried to make sudoku

[@alicewang5398]

same

[@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.

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[@i.i]

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

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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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They always do the easiest question on the internet.

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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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Ahmed01 I know !!!

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

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[@lovelya72]

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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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

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[@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

[@Yusuf-sy6rb]

For the first example you could do this faster by eliminating 2 variables at once by adding first and second rows. For a 3 variable system of linear equations you can always eliminate any 2 numbers in the same column and then use those 2 rows with the zeros to eliminate another number in a different column (which is always doable because you can just use LCM for any of the other 2 columns). This is way faster than trying to directly get it in row echelon form from the start because you can solve for any variable first, not just the third column only for example.

[@steadywatching7564]

Though you're really good, i wish you would explain "why" more often, even when it may seem obvious why a step is being taken.

[@LS19981]

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

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

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let's gooooo linear algebra!! i passed calc 1 because of you!!!!

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I'm literally skipping classes and learning from him

[@noelkuhomiemaihi5542]

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

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You've never failed me. I love you so much!

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I will pass my Discrete Math class because of you. Thank you so much!

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same

[@youssefbayoumi2694]

can i minus 2 rows ?? someone answer plz

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[@mr.creepz]

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

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Beautifully explained. Thank you. You are a fantastic teacher! I have watched a few of your matrices videos. I am a Maths teacher myself but I wanted to revise Gaussian elimination! Linda in the UK

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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 :)

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absolutely legendary ass guy. i cant believe im actually understanding everything clearly

[@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 ^^

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

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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.

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

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

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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

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I hope you will show me way through last year of my high school.

[@Antonio-z3n2p]

I think the right answer is (1,-1,2) you missed the negative sign on 2 for the first equation.( 1,2,3) does not satisfy the equation .pls consider my humble opinion.thanks by the way for all your lectures.I really appreciate it much! God bless!

[@abdulasad8348]

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

[@kazishahjalal6852]

Yes I have successfully done the second example on my own. Hopefully my life will be easier in university.

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[@murtazabasrawi4532]

In the 2nd example Z is actually equal to 49/13 not 39/13. I was trying to figure out what I did wrong and decided to just use a website to silve the equations and to my surprise, I was actually right. Thank's anyways. ❤ Wish there were more channels that share their knowledge and do it as clearly as you do.

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