Algebra - Solving Simultaneous Linear Equations by Gauss-Jordan Elimination 3 by 3

Visit ilectureonline.com for more math and science lectures!
In this lecture series I'll show you how to solve for multiple variables simultaneously using the technique called: the Gauss-Jordan Method of Elimination.
Problem Text:
3x-2y+8z=9
-2x+2y+ z=3
x+2y-3z=8

[@MichelvanBiezen]

Yes, you can start the problem by swapping row 1 and row 3

[@johnchong3017]

+Michel van Biezen the values of x y and z will be the same?

[@mahathikodicherla1234]

Yes

[@DJ-mr9tg]

Also, 4 minutes in, it'd be easier to first swap rows two and three before division, just to avoid fractions for a bit longer

[@lindseytraub8129]

I have been having a really hard time learning this method in college but i am so glad I found it! very clear and understanding!

[@MichelvanBiezen]

Glad you found our videos, Welcome to the channel.

[@Sami-xc5pl]

I prefer you sir as my online teacher than patrickjmt. Patrickjmt's videos are good but I found yours more thorough. I also subscribed :)

[@crayonman3990]

Best explanation of Gauss-Jodan I've found. Thanks!

[@404]

Extremely clear and easy to understand lecture. Thank you.

[@emmanuellekan3092]

10 yrs ago? Wow..God bless you.

[@MichelvanBiezen]

Thank you. God bless you as well.

[@Paul-zk6wp]

This was extremely helpful. Question though. If you switched row 1 with row 3 at the beginning of the problem like you suggested you would still come up with the same answer?

[@MichelvanBiezen]

Paul, Think of it this way. If before you convert the equations into the matrix format, you change the order of the equations, will it make any difference to the outcome? The answer off course is no. And therefore when you interchange rows in the beginning it has the same effect as changing the equations before starting the problem.

[@elangz9201]

Hi michel, just wanna say that we rlly appreciate u teaching us! Ive been watching your video since the 1st year of senior high, and now im doing masters program and still watching 😂

[@MichelvanBiezen]

Thank you for sharing. We are glad y🙂ou found our videos helpful throughout your studies.

[@mjdc2505]

He made that hard ass problem look easy and way more understanding.

[@AllthingsEssence]

Bruhhh so much work omg ! We won't even use this in the future ! Who made this up

[@Breonaleonard]

All things Essence MAAAAN the truth! Just stupid

[@rluximon]

Thanks very much, you help me to understand this method very well

[@MichelvanBiezen]

Glad it was helpful 🙂

[@J03y805]

I found it easier once you find the first 3 zeros down by the left corner. after that just back substitute. original problem 3 -2 8 = 9 (leave first line alone) -2 2 1 = 3 (2xR1 + 3xR2 -> R2) step 1 1 2 -3 =8 (1xR1 + -3R3 -> R3) step 2 3 -2 8 = 9 0 2 19 = 27 from step 1 0 -8 17 = -15 from step 2 3 -2 8 = 9 0 2 19 = 27 0 0 93 = 93 ^(4xR2 + 1xR3 --->R3 ) step 3 using the second matrix 3x - 2y +8z = 9 3x -2(4) + 8(1) = 9 x=3 2y + 19z = 27 2y+ 19(1) = 27 y=4 93z=93 z=1 This was easier for me and less work. Hope this helps.

[@John-ye8sj]

good point, I learned it exactly like you said in highscool

[@incrivel1216]

that is gaussian elimination method. Gauss-jordan requires both above and below diagonal to be zero in order to solve for the values. although you can use that method but it is entirely different topic which is gaussian elimination.

[@itzelbarrera9172]

I am taking a fast paced class this semester, unfortunately I was ill the day the professor taught this and was left so behind! thanks to this video I completely get it now! thank you :)

[@NOLAWAGAINSTIT]

best explanation I've seen so far.

[@MichelvanBiezen]

Glad it was helpful!

[@paramedic7024]

I knew something was amiss. My lecture was fine. But this showed me a structured way to solve these equations. Thank You

[@jasonheard2436]

I just took Physics II for engineers this summer, and really appreciated your videos. Now, I am in Linear Algebra and very happy to see that you have videos for this course also!

[@benjamintoroa1223]

Very good explanation Thank you

[@MichelvanBiezen]

Glad you liked it

[@xfronwenzyoucamex]

I'm almost getting it now. Thank you for your tutorial.

[@livfrazier6295]

Your videos are very helpful. I really struggle with this, like more than most people. How do you know what to do to numbers in order to get reduced echelon form? You always know multiply this by that to get this, etc., so I'm just wondering how you know to do these things... that's what I struggle with most with this.

[@MichelvanBiezen]

+Olivia Frazier Solving any math problem is usually a combination of knowing what to do (meaning the steps you must take to get to the solution), and then how to do it, (meaning what specifically must you do in order to accomplish each step). Go through the problem again and let me know what specific step appears confusing. (I am trying to narrow down what exactly is giving you trouble)

[@lift6301]

I have the same problem, it's trying to figure what steps to take to turn that number into a one or a zero that always takes me awhile. In the video you mentioned "using the correct rules". Is there a place where i can learn what these rules are as they will make solving these 3 by 3's a ton easier knowing what i can and what i can't do. Awesome video by the way really helped me understand :)

[@emadnabil8579]

What is martingale betting system and does it affect in bussines probability?

[@hadisyetegu2056]

wow you are brave man I am appreciate you just continue thank you for helping me

[@MdLamimAhamedRiyad]

Alhamdulillah,now I am clear.Thank you very much ❤❤❤.

[@MichelvanBiezen]

You are welcome 😊

[@HYBECTIVE]

We use to do these everyday in Engineering Analysis 1, and here I am again this time in Engineering Analysis 2 forgetting how to do these lol. KZbin is great!

[@abdullazeezsalehibrahim8753]

Well done ,very educative

[@kalpanaakunuru2122]

Thank you sir excellent explanation I tried many problems by using your method I got the answer

[@adrianesquivelocampo8234]

Not necessarily, he would have to swap 1 & 2 if needed. Other wise it could be left like that.

[@muaazismail_]

Great explaining

[@StrangeParticl]

thank you thank you very much. I like the way that you did the lesson... that is the easy way to do that..

[@santoryu8940]

Any tips for less fractions when performing elementary row reductions?

[@MichelvanBiezen]

There are no hard and fast rules, however, I will go back an try a different step when I see a lot of fractions appearing. Also certain fractions are easier than others (1/2) is better than (1/3).

[@vishnutejaanandam8053]

I've so far seen many videos but this video made me undersatand.

[@rodericksibelius8472]

I have never liked the Gauss - Jordan Elimination method, it's so confusing to me, I always resort to the old CRAMERS RULE as taught to me at my Two year course in Electronics/Electrical Engineering Technology mathematics. Back in THE MID 80s and 90s, "Qbasic" was included on the Microsoft Operating systems and I wrote a CRAMER's RULE program for my own use. Nice to know that method but as an experienced Technician, I have never used GJE. LOL. Now we have CASIO, HP, SHARP, Scientific advanced calculators so CHEAP they can crank the answer within a few microseconds = I just have to PLUG and CHUG.

[@MichelvanBiezen]

Yes, the tools are great these days. These videos are made so you can understand how the method works.

[@rashidissa5887]

I have only an O-Level (Cambridge 1967) and now in my late 70s. Never did matrix then but started learning only lately. Very interesting and almost have known all the methods of solving matrices. Iam surprised you, younger than me perhaps, to finding difficulties in either process. Have tolerance, maths most interesting subject

[@PlamenUzunov1]

thak's, you are THE MAN!!! I have a exam very soon...

[@dedesurachman10]

Thank you. It's very easy to understand the method..

[@MohammadAlshahrani]

Good job

[@MichelvanBiezen]

Thank you. 🙂

[@loly19951]

thank you very much

[@DarknessIsThePath]

Is the purpose of this to get the "Identity matrix" to have definitive answers for the 3 variables?

[@MichelvanBiezen]

Yes, it is the method to solve the three equations simultaneously for the 3 variables.

[@DarknessIsThePath]

Michel van Biezen Ok thanks :)

[@hexaCode0]

Thank you very much! It helped me a lot! ❤️❤️❤️

[@MichelvanBiezen]

Glad it was helfpful. 🙂

[@JM-fr9bc]

why can't you just take the same approach as a matrix with two variables and start by dividing the first row by 3?

[@MichelvanBiezen]

The best way to figure that out is to try it and see if you get the same answer.

[@shweta335]

Thanx... sir, now i understand this concept.

[@midas5616]

I tried this with -x-2y+z=-12 -x+3y-3z=13 x+y+z=1 idk what i did wrong, i exactly did every step that you did and i didn't get any zero.... any help? let me know what i did wrong

[@MichelvanBiezen]

It should work. (you probably made a simple error) the answer is: x = 12.5 y = -4 z = -7.5

[@GabrielaLealPinheiro]

Finally I understand.. Thank you so much for the video

[@mbamshizle]

SO to you michel!!!! very usefull video! ty!

[@PotatoTacoman]

What about using a calculator to solve the problem just wondering what you think about using rref( on a ti-84

[@MichelvanBiezen]

+frankbradshaw1770 Those TI calculators are great. The point of these videos and this type of material is to learn how they work. It is the steady accumulation of understanding that helps us prepare for the future.

[@HerLifee]

YOU MADE THIS SO EASY FOR ME!

[@Mithrandir-]

Can this method also be used for 4 by 4?

[@MichelvanBiezen]

+Armin Ajdarpasic Yes, it takes more time but it works great with 4 x 4 as well.

[@Amr-hb2wh]

Sir , you are a legend . Thanks !!

[@ahmaddzulhakim4189]

is the formula getting the 0 and 1 fixed or depends?..

[@MichelvanBiezen]

We didn't quite understand the question. The goal is to turn the matrix into the one shown in the upper right corner.

[@ahmaddzulhakim4189]

@@MichelvanBiezen its okay now..im clear crystal..thnk you for your concern and keep the good job

[@Capt_Vic]

Thank u for making me understand this in simpler way. :)

[@GarbanzoBeansFan]

thanks a lot.... very much appreciated

[@badguyfromstarwars]

I can't find the three, 3, other videos working with these kind of problems..

[@MichelvanBiezen]

Darth Wader You can find the other video, by typing: "Michel van Biezen Gauss Jordan method of elimination" in any search engine ot by looking at the list of "Most popular videos" on my channel. I believe there are only 2 examples. I'll have to make more when I get a chance.

[@_Crazyslots]

i felt like this is harder than calc😭😭 interms of annoying steps, btw great lesson:) absolutely love it

[@jananathbanuka4994]

Thank you very much Sir :) Really understandable

[@kathimusalaiahcrp625]

Thank u sar please uploaded more videos

[@HaileyRox0099]

thank you so much you are a sweet angel

[@Vpantera92]

you are extremely helpful thank you!!!!

[@FallenAngelMMA]

Thank you!

[@MichelvanBiezen]

You're welcome! 🙂

[@gracianodelgado3774]

You're the best!!!

[@didiruhyadi4798]

Helpfull thanks

[@Vpantera92]

you be willing to do some dynamics problems?

[@MichelvanBiezen]

+Jesus Valles What type of dynamics problems are you interested in?

[@zhariamccoy2044]

Thanks so much

[@ral2585]

I dont think you would need to make the top right row 0,0,0. only the left bottom row as you can do simultaneous equations instead of writing more

[@MichelvanBiezen]

Those are 2 different methods. You are referring the the reduced row echelon form.

[@ral2585]

Michel van Biezen Difference?

[@MichelvanBiezen]

We teach both method. After that it becomes personal preference. (There are 7 methods used to solve linear systems of equations).

[@sisitoutailongani1437]

thanks for the video really helpful cheers

[@musasizisolomon9980]

Thanks lots

[@MichelvanBiezen]

Glad it was helpful! 🙂

[@kufreetim7100]

Thanks

[@MichelvanBiezen]

Welcome

[@HelloZito]

Thank you for your nice explanation :D

[@jamiecqwong]

Thank you so much breaking down the problem, step by step and for posting this video! It helps a lot! :-)

[@Tony-nl6pf]

There's so many different way to do this and every which way I do it I get it wrong. You know the steps to do it before you started the video. Pick one and do it naturally.

[@RachelAbereOkpulor]

very helpful..

[@jananathbanuka4994]

Hi :)

[@rico-en]

Thanks brodie

[@PadelManiaZzZz]

Thanks you very much !

[@ruatdikac736]

You save me from my exam

[@alfredcalleja450]

Brilliant: thank you!

[@LuisVivar]

Thanks!

[@arinaazyr6347]

thanks sir

[@collectiveguitar8]

Thank you Thank you so much

[@denverchamberlain9657]

this guy is a fucking slayer

[@Lucky_razberybun4657]

Your a god🥇

[@MichelvanBiezen]

Not in the least. Just a simple man trying to do his part. 🙂

[@MarkTaban-lp7xn]

The video is blurred

[@MichelvanBiezen]

We just checked the video and it looks clear to us. You can change the definition on the settings button in KZbin

[@Harbingerintheflesh]

Thank you!

[@pramishkhanal635]

Nice

[@FrancisPauloTV]

Splendid! :)

[@sharearzahid8821]

Yes

[@khaleditani5230]

THANKS !!!!!!!!!!!!!!!!!!

[@collectiveguitar8]

I got my problem off by a mile but hey thanks for the explanation

[@priyankadhurwey492]

video is not clear

[@jonathanmoulin8660]

tyvm man

[@abdifatahshibrahim90]

Your Blackboard is very far please come near with our eyes

[@vaultmafia6725]

Easy peasy lemon squeezy :D

[@nihalaky]

çok güzel anlatım teşekkürler

[@MichelvanBiezen]

+Nihal Akay You are welcome.

[@Aupaatleti33]

thanks anyway

[@AbundantRick]

Bruh 12:34 still doing 2nd problem out of 12. Im finna just take this L

[@JohnnyYenn]

Support Michel van Biezen on Patreon!!! The man is a saint! www.patreon.com/user?u=3236071

[@panzznine713]

its hard but ihave to learn it anyway for a c program lol

[@MoMo-gm4cf]

خاب الصوره بعيده هيه شنيه

[@lg7480]

Gracias! ^_^

[@juniorjay001]

you went way too fast. and you should not do multiple steps at once! teaching 101 dude

[@ssebitaabawamala6861]

Too dim

[@MichelvanBiezen]

Yes, we had to learn how to manage the light conditions. We are better at it now.

[@karmaamour3870]

To complicated thoe didnt help at all

[@karmaamour3870]

+Karma A'mour ill stick to the regular way of elmination

[@Vpantera92]

+Karma A'mour find another major if you don't understand it..... this so easy to follow !!!

[@karmaamour3870]

Jesus Valles who asked you like.... really i didnt understand it this way i understand it another way and thats elimation you find another person to be a troll to

[@spo154]

+Karma A'mour you are just stupid

[@karmaamour3870]

agustin Bilancetti twistedblktrekie i have ma own way of doing it ... to be honest i dont understand this method.. im only in 9th grade but im taking Math 1100/Algebra III so im kinda advance.. so please stop making it look like im stupid because i dont understand this method everyone doesnt learn the same and i would appreciate if you guys help me instead of bring me down. Thanks so much :D

[@deadweeboo7745]

THANKS A LOT

[@philiplouisendiape9490]

Thank you so much. . .