❖ Using Gauss-Jordan to Solve a System of Three Linear Equations - Example 1 ❖

Using Gauss-Jordan to Solve a System of Three Linear Equations - Example 1
In this video I solve a 3 by 3 system of linear equations with three unknowns.
Here we use Gauss Jordan to solve the system of linear equations.
To perform this method, we can switch out rows of our matrix or add constant multiples of one row to another row.

[@patrickjmt]

Hi all! Please post comments, questions and anything else on your mind in the comment section! While I try to answer as many questions as I can, there are more questions than I can answer by myself so if you are someone who might be able to help, please do so! The community is so much better when everyone is involved and helping each other out. Our strength is our willingness to help each other! Also please feel free to like or dislike the video. Your feedback is always appreciated so that hopefully I can make my future videos the best possible! Thanks and happy studies!

[@aisyahsuhaini881]

vector please :((

[@battlemaniac007]

please can you solve one question for me with explanation? The question is: 7x-4y=1 4x+2y=-8 by gaussian elimination method

[@secondgensnark7060]

Umm 10+(-6) does not equal -16

[@fazeranimation3216]

Do you have a Chanel on social media like Facebook?

[@emananwaar2882]

patrickJMT can we also use Cramer rule

[@raymondhill7837]

Gauss-Jordan elimination is such a royal pain in the ass! Argh! :(

[@barcacrazy99]

Normie here v

[@riyadulislam9832]

Very very true

[@ARNAKLDO]

yeah lol, but at least it is not like combinatorics. That thing seems like ancient hieroglyphs to me..

[@salvadorsanchez5887]

Its cos u black

[@III-ip8uc]

Your IQ is low then..

[@jeffjaco]

I took this class in college it made no sense than, and 13 years later it still makes no sense. It seams like he is just pulling numbers out of the air. How do you know what to add to what, what to multiply by what

[@srpwny6095]

you don't need to pull out the identity matrix to solve this kind of problems, you only need to convert the matrix to an identity one only if you want to find the inverse matrix

[@rokbleki3929]

You need to look 1 step ahead. You adjust the rows so you get 0's under the left side diagonal. How do you get 0 with 1 and 2? You multiply 1 with -2 and add it to 2.

[@thetheoreticalnerd7662]

This is really simple to me, as a 12 year old

[@akashskumar99]

common sense

[@jeffjaco]

@@akashskumar99 But aren't there other ways to arrive at a number? How do you know you will get the correct end result?

[@philmoore4238]

For those who were asking .... Gauss first had a method of solving systems of linear equations using matrices. That method is known as the Gaussian method. It is also known as row echelon method. Jordan refined Gauss's method. So we have the Gauss-Jordan method. It is also known as the reduced row echelon method.

[@The228Bassplayer]

This would be a little easier to understand if you said why you did each step and weren't combining steps.

[@lewisjones284]

To people who don't understand this video, you need to be familiar with matrix row operations. Here is a quick summary of how you can modify your matrices: n = last number of row Matrix multiplying: You can multiply any row by any number, and you can multiply it by decimals, meaning you can technically divide. Matrix division as a concept is undefined, but multiplying by a fraction isn't. Example: row 1 = row 1 * 2. Every entry in row 1 gets multiplied by 2 Matrix addition: You can add a row to another row. This involves adding every equivalent value from one row to another. Example: entry 1 through to entry 'n' in row 1 gets added to entry1 through to entry 'n' of row 2. (value by value, row1 entry1 + row2 entry1, row1 entry2 + row2 entry2 and so on.) You can also add a multiplied row to any row, as multiplication is reversible. Example: 2*row 1 gets added to row 2. Matrix subtraction: Negative equivalent of matrix addition. No example needed. Matrix row swap: You can swap rows with any other row at any time. Example: row 1 -> row 3, row 3 is now row 1 and row 1 is now row 3. Hopefully this helps clear up some of your questions on what is going on in this video.

[@kiirajangmk-gh2uk]

your ability to connect with us, provide support, and inspire curiosity through a screen is truly remarkable. You have made learning accessible and enjoyable, turning challenges into opportunities for growth. Thank you for your unwavering commitment and for making a lasting impact on our education and live

[@DaDumFriek]

Patrick....you're really awesome. I was stuck on a problem for the longest time after doing calculus for two years and I totally forgot that you could switch rows. That literally saved my life when it came to solving the problem. Thank you very much!

[@jointsatv8802]

YOOH THANKS SIR, I AM NOW MASTERING THAT PAIN

[@patrickjmt]

+Khutso Morgan own the pain

[@Triplechoco52]

If your brain isn't hurtin', then you're not learnin'

[@smahane5664]

+Intelligent Cosmic Being I agree with you, I love math

[@khalid-jp4nz]

hurting soo much lol

[@nabeeldraws506]

This video is nearly a decade old yet it cleared every thing I missed out in class on this. Great video Patrick! 👍

[@patrickjmt]

that is the good thing about math: it doesn't expire :)

[@dapjnekerem2945]

I was struggling with this a lot and every other channel was using weird random formulas to solve these that were super confusing. I really like the easy no-bullshit way you did this. Thank you so much!

[@akashskumar99]

helpful for backbenchers like us trying to study at last second, keep postng simple stuff like this,cause thats what we actualy need, and not some 3hour lecture

[@Happy-oh6jb]

Patrick, you are a great teacher solving the question systemically. Thanks

[@overthinkerstinker]

I like that you show what you are doing at the end of each matrix (ie R2 + R3..) not all instructors "show their work".

[@blackyang925]

how do you know when you're suppose to interchange the rows? do you do trial and error first?

[@shreeshenoy6629]

No, its because we want 0 in the upper side as well as in the lower side. So we interchange the rows by checking 0s

[@jedza6303]

Thanks

[@damiccathedesigner]

Thanks a ton! I watched other videos before this one, and they all weren't explaining the steps enough. This was the first one I've found that really helped!!!

[@Vanessabluevulcan]

I was hopeful that you would have a video on this, and as always you never fail us Patrick!

[@NVGamingOwl]

You're opening up a lot of possibilites that my book is not even telling me. Thank you! Likes and a sub.

[@Shoobedooby]

Why is it that when I watch videos of Patrick I am able to easily grasp what my college professors take 1 hour to explain... Thanks for making life easier.

[@nancywaithira4378]

Wow.. understand it in 10mins...my lecturer spent more than 6hours explaining the same...thanks so much professor

[@JDMcivicR1]

Thank you Patrick!! I've watched your videos all through calculus and now discrete math.. You are awesome!! Saved me Again!

[@muhammadomar997]

great video,but you didn't explain much as to why you took some steps

[@alexshabu4540]

you are 100 times better than my teacher

[@joseguillermocruzrodriguez8243]

You are a life saver - thank you for clarifying the Gauss-Jordan left side identity !!

[@eruna9540]

THANK YOU FOR MAKING IS EASIER!! My prof teach this in class and he went way too fast that everyone was confuse. But thanks to your video, is easy now

[@patrickjmt]

glad i could help out :)

[@HynoHypoMan]

Thanks sir patrick.... Your explanation is far more easier for me to pick up the concept way better than my own teacher. Thank you.

[@foreverfaeriejoy]

witchcraft

[@essykwamboka1]

😅😅😅😅😅you not serious

[@zacharygippe7873]

Thank you. You do it better than my math professor at Eastern Washington University!

[@al8905]

sat for an hour in a class and couldn't understand a thing, thank you for this

[@limitless5337]

You did it again my friend. It would be great if you explained how one can see if the system of equations is unsolvable

[@rafidahabdulkadir76]

thnk u fr existing patrick, we need more ppl like u in this world

[@samtbarber1]

Main issue, is that in Matrices you cannot actually divide numbers, it doesn't really affect it here but where he divided row 2 by -5 is incorrect. You can only multiply and add. You have to multiply by -1/5 (which is the same as division in this case but in certain circumstances division will give a completely different number, especially in higher math with algebraic matrices)

[@masift1494]

I know this video is old, but I see a lot of comments complaining that this its still "too hard" and that you didn't explain it well enough. These people clearly don't understand that they need to try it themselves and follow along if they want to have any chance of figuring out how to do it themselves. Practice makes perfect. Great video Patrick, I have a test on this tomorrow, and this definitely helped me out.

[@Dark4994]

godness, and our teacher spending so much and no one get it. thank u so much

[@deepkaur5654]

Easy to understand and nice explanation

[@techny3000]

Thx this really helped a lot Btw thx for explaining that the columns that are done don't change

[@HeatherRoseMusician]

Thank you Patrick! for the first time ever this makes sense!!!

[@patrickjmt]

wonderful :) glad i could help!

[@JosephYuonfaa]

Thank you sir,you cleared all my doubts. Please upload more videos to help we those that are still learning.

[@junotanner-allen1481]

why did you interchange them? You need to explain whyyou are taking the steps you do

[@TheFlatlandsS]

Because of the zero on the z-axis. For this method of solving a system you need all zero's except on the diagonal.

[@afrosymphony8207]

ohhhhh makes sense but still u can add 2 later and stilll change it

[@trace8617]

because the third row looked closer to the identity matrix’s second row

[@qolbola_bilimuz4424]

thank you brother, you have been always helpful. Keep making vids like this

[@patrickjmt]

Thanks, will do!

[@alinakopbaeva5558]

Haha, thanks for the video!! I've been watching some of your videos during the break and when classes started again we were covering these topics! This stuff is really easy, just requires some work. If you think it isn't, don't be lazy and practice practice practice practice.

[@laurathesingerandsometimes3001]

The sharpie😂😂 I love that he feels confident enough to use permanent ink…..waiting for that confidence myself 😂

[@bhavyas9772]

I have seen 10 vedios on this ur best.. Love from India Andhra Pradesh..

[@patrickjmt]

thanks!

[@bro-ken5709]

Same ( intermediate 1a sucks 😩 though)

[@jairusalubin4069]

using this formula right now during lockdown on my home learning kit

[@marynellnarciso7866]

I'm doing this right now for College Preparatory Math for my senior year and its sooo confusing! Thankfully this video made me understand a little bit (:

[@kostastsigkounis8784]

Better than my professor :) Good job !

[@arshia1698]

Loved the explanation ! Helped me so much!

[@HeplingHandGaming]

Here's my peace. I am in school at Ohio State. My instructor for linear algebra is 70 some years old, has an accent and talks into the board. Nobody can understand what he says. It would be nice if he realized this, but instead, he yells at us for asking questions. "Use your brain, not mine" was an EXACT response to a question. I have absorbed more from you than my helpful teacher. Thank you!!

[@alberto0795]

Does it matter if you interchange the rows? or is it just easier?

[@Truthkills002]

amazing!!! thank you!!! freaking out before a midterm and this helped alot

[@justdnk777]

Wow. This is going to take awhile to get good at. Thanks for the video Patrick.

[@aZn0vvNz56]

Basically, the rule is you can add rows together and still have a equivalent matrix, as well as multiplying a row itself with a non zero number (in this case row1 with -1 and -2). So because you want zeros in the first number in row2 &row3, you can multiply row1 with -1 and add to row2 and multiply row1 with -2 and add to row3. Hope that makes sense.

[@carmenhill8645]

This is very easy stuff. Thank you for posting this. God Bless You.

[@rnj5890]

easy? lol not for me

[@kamraman123]

i really like your explanations. youre also very articulate imo. thanks

[@samychihi21]

BIG THANK YOU MAN FOR THIS SERIES OF VIDEOS I really appreciate that :)

[@VIR092]

The Gauss-Elimination is certainly a captivating and definately an effective of means of matrix calculations, once you get the dynamic of it down it really is a cool tool to have.

[@danielhernandez-vo9zc]

Thanks! Made it a lot clearer to understand!

[@lalita2688]

Awesome. Thank you so much. Your teachings make me love math even more.

[@StateGenesys]

great videos man!! I take on online college algebra course, and i could never learn it from the examples they have there. But watching your videos made it so understandable.

[@lordbow]

Excellent video! The algorithm makes sense now. I would just recommend putting some comments on the video stating that when doing -a*rx+ry, you want to use the constant -a from the row where you'll be putting the new values: so a constant -a from say row three, times the row 1 will place it's new values into row 3. Great video none the less!

[@anishmanchanda4988]

Plz Explain the conditions for consistent and inconsistent system of equations as well. basically..How to find whether a system has no,unique or infinite number of solutions??

[@CoreTech951]

Thanks dude, I have a Python programming exam tomorrow at my mechanical engineering college and I'm just learning this if I'll by any chance have to program it

[@pma_fx7290]

11years after still helping ❤️

[@warcraft3kokil]

Thank You.Your video is easy to grasp. though i think at 6:10,we can use R1-R3=R1.

[@TheHawtsoup]

Can't we stop when we get row 1 equal to 0, 1, 0, 2? This would make y=2 and we can use that to solve the rest? I don't understand the advantage of Gauss-Jordan vs. Regular Gauss. Cheers Patrick.

[@priyansudash]

Hi sir i m from India I love your video. Ur videos help me alot thanku so much. Keep making such amazing videos love from 🇮🇳

[@emmeva1]

Thank you very much!!! this video has become my hero!!! at last i can understand and get my points on mid-tearm exam ^_^

[@whatsinthis2846]

You did a really good job explaining it! Thank you

[@yannachi322]

i actually solved it in a different way but ended up with the same answer.. Anyway, this video did really help me solve those equations easily. Nice work!

[@nobodynobody5374]

i think i'am gonna learn a lot through your channel.

[@liamparkin3817]

I didnt have sound and still found this better than my maths teacher!!

[@alijoueizadeh2896]

Thank you for your time and effort.

[@awra.v]

thank u very much. it helps a lot~~~ tomorrow i have math mid-term exam n i really need to know this gauss jordan thingy~! >.< thanks for uploading!

[@ph.sameerhabeeb2794]

Thanx patrick for this video you make it so easy

[@sixteengaming1352]

In Gauss Jordan method we have to solve till we get principal diagonal 1 rest zeros 1) try making zeroes on bottom corners of the sq matrix 2) later try making 0s on top corner

[@patrickjmt]

@23youwatch whatever is on the right side of the equal sign is what gets updated

[@shavendhavin]

sir if we did not change the row 3 and 2 would it change the answer and thanks because your tutorial is easier to understand

[@amazingvideos1760]

I wonder why all these ignorant people disliked this video!? Any way keep moving forward man! Thumbs up 👍 for ya really good

[@cantcount0]

wow that's just kinda simple, thanks. i dont know why in books they use all these complicated annotations that confuse the heck out of you!

[@violet20205]

Thank you so much i can now understand which step to take !

[@EEEClubtech]

hello ?

[@mikays3580]

Thank you so much for saving me from my ineffective professors 😩❤

[@ShakuRrhymes]

Please do a video using Echelon and Reduced Echelon. Thanks for these helpful videos!

[@patrickjmt]

Pretty sure I have

[@furqanashrafi7746]

very helpful tutorial, GOD bless you sir

[@philbot01]

Thanks Patrick!!! Just letting you know, My name is patrick, I like maths AND i'm left handed too. We have so much in common!

[@froet213kil]

emm, is there any advantage of using the gauss jordan method instead of just using the conventional method ie. eliminating some terms?

[@xcompa77x]

god bless you for this work you do. you bring peace of mind and confidence to so many. you shall be rewarded for it i know it. right this moment i am cramming for a test and maybe i won't fail my college algebra. my prof was taught by a nobel prize winner for his doctorate in math and he drives me crazy. they should give people like you the prize you are better. keep making vids!!!

[@anthonygreeko4309]

Since you could take a row and divide it by 2 (i.e. R2/-2) Can you take a row and add or subtract a number? i.e. R2 - 2

[@Likwidl]

good job man even though you could've not gone all the way and solved until u reached the identity matrix the first step was enough

[@DawgFL]

What's the difference between this and "row operations elimination"?

[@Republic1ders]

Thanks for making my 2 grueling weeks of matrices easier =)

[@risajajr]

What kinds of validation should you do before using this technique? For example, given the equations x + y + z = 2, 2x + 2y + 2z = 4, 3x + 16y - 5z = -15, the technique breaks down as the first two equations are essentially equivalent. Also, there could be cases where their is no solution for the equations (they might never intersect).

[@patrickjmt]

yes in this case you will have a free variable and infinitely many solutions.

[@05dabest]

is this basically row reduction in echolen form?

[@abdifatahshibrahim90]

Fantastic Thanks for your explanation Mr Patrick

[@abdihakinahmed2817]

thank u sir. I have exam of linear algebra tomorrow (23August2016) at 11am, now when I watched I got the point that I was confused

[@johnfedorov8089]

how did it go?

[@SNDP213]

Abdihakin Ahmed Yeah how did it go?

[@NateMicahTV]

yeeah, how'd it go?

[@MiguelMartinez-yj7yu]

so, how'd it go?

[@addyhernandez9272]

Forgot to ask. How’d it go?

[@geraldchristophers.espino6576]

Thank you Patrick, now I understand how to solve Gauss-Jordan theorem. :-)

[@janmarsh4104]

Patrick, you are my new favorite human, thank you!!!

[@iiAnbuii]

Congrats, you murdered my brain.

[@295laanne]

thnx for these simple yet very helpful tutorial...

[@patrickmc7486]

Very helpful!!! My exam is in an hour and now I know what to do! Thanks!!!

[@radekpilat7892]

Good stuff, nice and easy examples but in my lectures if i write R1 - R2 then i perform the calculations on row 1, you do it the other way but it's still making sense ! :)