Algebra - Solving Linear Equations by using the Gauss-Jordan Elimination Method 2/2

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 + 5y = 9
2x + 3y = 5

[@TheDemon1496]

You, my friend, just saved me from great confusion.THANK YOU!!!!!!!!

[@harmandhillon86]

After hours of having a understanding of the Gauss-Jordan Elimination, you sir FINALLY were the one who helped... Thank you so much sir!

[@MichelvanBiezen]

Great! Glad you found our videos! 🙂

[@plasmakitty6390]

right?? there is no help out there with this freaking method its so confusing and exhausting

[@candicefree6986]

I hope this isn;t taken the wrong way...I am above and beyond stressed about about finals in a few days but clicking this video and hearing you sound like Gru just TOTALLY MADE MY DAY!

[@MichelvanBiezen]

No, not at all. You are not the first one to mention that I sound like Gru. :)

[@keletsomalatjie353]

After so much confusion, you have helped me understand this so much better! Thank you!

[@MichelvanBiezen]

Great. Glad you found our videos. 🙂

[@hirahasan21]

You explained this so well! Thank you for taking the time out to explain this step by step.

[@MichelvanBiezen]

Glad it was helpful!

[@amplemind9739]

You made it so simple, why can't all books and teachers be like this. Seriously spent weeks trying to figure this out and it took you all of 5 minutes and 5 seconds to demystify it. Thank you sir!

[@samsonk2077]

Thank you so much. I couldn't have done my homework without u

[@MichelvanBiezen]

Harriet, Good luck with your final!

[@Enyogfx]

my right ear feels neglected

[@MichelvanBiezen]

Apologies...When we first started our KZbin educational channel, we had ABSOLUTELY NONE, ZERO experience in video making. We were math/physics not film-making majors. So we had absolutely zero clue about stereo sound. Fortunately we do have a learning curve. So our “less old” videos are in stereo. A viewer suggest this: for anyone with problems with mono audio, just plug the headphone jack half way in and it will make it stereo, remember to plug it back before, after this video or people around will be listening to your device too!

[@Yolowhy]

Thank you so much for sharing your knowledge. You have made this concept very clear better than my own math professor. :)

[@shariqueiqbal6046]

who is your professor, it is a very easy method,, my professor is awesome

[@joshuauribe1823]

thank you so much this really helped me, and lets be real this video deserves more like than it has

[@TheShmadison]

Thank you for doing this. You have helped me so much. Keep up the great work and thank you again!!!

[@MichelvanBiezen]

Glad this is helping. Keep up the studies.

[@klym8_]

thank you so much! i have an exam on this tomorrow

[@milkcreightronny]

Having never seen this method before, this video gave very clear steps and explanations for those steps. thanks vmuch

[@MichelvanBiezen]

Glad it helped!

[@terekaguerrero6791]

Thank you so much for breaking this down for me, I was so confused before this video I APPRECIATE YOU!!!!!!!!!

[@MichelvanBiezen]

Glad it was helpful!

[@eduardomartinez5775]

just helped me out BIG TIME thank you!

[@mariumhabib7209]

will get good marks now. All thanks to you sir

[@selenireyes4446]

Thank you so much!!! This is very helpful indeed!

[@riatardieu5624]

I have looked at this video a lot of times and I was only able to complete half way through some of my questions. I need help!!!!!!1) Express the following system of equations in augmented matrix formx+2y= -1 2x+4y= 1 2) Express the following augmented matrix form as a system of equations with two variables.7 1 I 10 -3 5 I 0 3) Express the following system of equations in augmented matrix form:8x+3y=2 5x=17+6y4) Solve the system of equations represented in augmented matrix form, using Gaussian elimination.5 7 I 6 10 -3 I 46 5) Solve the following system of equations using Gaussian elimination4x+5y=7 -2x+9y=316) Graph the inequality in the given coordinate system, using shading to indicate the solution region. 3x+4y

[@pokeypoke81]

You are great at explaining this!

[@alitariq360]

Great explaining Question tho Do you have to use the gauss form by a line e.g like can you start from the bottom right as well?

[@MichelvanBiezen]

It is highly recommended that you start at the top left as shown in the video.

[@davidsupersac]

thank you very much! it is really helping to understand this tricky resolution...

[@bris5773]

This video saved my life

[@idontknow-ms8mc]

This video is great, thank you!

[@HarrietOakley]

Thank you!! My final is tomorrow. I never understood this!!!!!

[@agjilfbb88]

Great job teaching and explaining I appreciate it.

[@simondelagarza1429]

thank you for the help, I literally would've failed without your guidance in this lesson.

[@MichelvanBiezen]

Glad we could help!

[@abuslje]

Top Teacher!! thank you!

[@acerzz2287]

How do you know which one x equals and which y equals? Like how do you know y is 3 and not -2

[@MichelvanBiezen]

You can change the order of the equations and you will get the same result. The order in which x and y appear in the matrix is set and determined by the format of the equation.

[@nanarisandia1123]

It helps a lot! Thank you

[@phungongoc9980]

It was very useful. I understand how to do it immediately after watching this video. Thank you.

[@MichelvanBiezen]

Great! Glad you found our videos. 🙂

[@bakhtawarniaz3151]

what would I go about this if the first coefficient(upper left) is a zero?

[@MichelvanBiezen]

Then you start by moving the rows up and down.

[@ashleegarrigan3309]

Very helpful, thank you.

[@lenny_freestyle5237]

thank you so much for helping me! , now i am gonna pass my exam for sure!

[@MichelvanBiezen]

All the best on your exam.

[@MCchanelll]

this helped me! thank you

[@OsagieGuobadia]

My professor learns this method today in online class. Now that I have took the picture, I will study it.

[@MichelvanBiezen]

All the best

[@lanyero1]

thank you for your help

[@atheera1072]

5:18 why doesn't the 1 change? shouldn't the whole row be multiplied by -5/3?

[@MichelvanBiezen]

Row 2 is multiplies by -5/3 and then added to row 1. Row 2 remains the same.

[@halimahassan8854]

thank you very much !!! it was very clear

[@MichelvanBiezen]

Glad it was helpful.

[@kaustshroff381]

Thank you so much sir! Watched couple of different videos on Gauss Jordan but this one was the most helpful. Very thoroughly explained. Keep up the good work!

[@manantrivedi5622]

Saved my life

[@biggiemary9528]

Thank you so much. You saved me from confusion.

[@lookaa3472]

Thank you so much 👏🏽❤️

[@abmuqeet08]

Excuse me, Sir! Can our first step be like ( R1 ---> -R2+R1 )?? Because in this way we can also get (1) at top left??

[@MichelvanBiezen]

Yes that is a good step and you will get the same answer. Try it.

[@abmuqeet08]

Ok Sir, Thank you :)

[@roxx_lee8834]

Fantastic!!!!! THANK YOU SO MUCH!

[@MichelvanBiezen]

You're welcome!

[@TheYazeed1996]

Very helpful thanks

[@sahabudinamilil4046]

When you turn into R2 why did you changed the positive 2 into negative 2? Can enplain it why? I'm so confused.

[@MichelvanBiezen]

That is the technique. In order to turn a number into a zero, you take the negative of the number, multiply it with the row containing the zero and adding it to the row with the number you are trying to eliminate. If you look at the 3 x 3 matrix elimination method you can also see how that works.

[@sahabudinamilil4046]

Ah okay now I understand. after we found the 1 in the first row in the next is 0. In the second row 1st digit number it will be always changing it by positive to negative? Sir thank you so much and Sir do you have Lecture videos about ''Limits and continuity''

[@MichelvanBiezen]

That is covered in the introductory chapter in calculus: CALCULUS 1 CH 1 LIMITS & DERIVATIVES kzbin.info/aero/PLX2gX-ftPVXVzRDO_yw83HFddu5rfWsOX

[@user-zi7kp8un3s]

wow! excellent video!

[@MichelvanBiezen]

Thank you very much!

[@xeldaxloveyouira379]

Thank you!

[@CarlosSerrano-fp4zz]

excnt explanation thank

[@iloveallah7896]

God bless u sir

[@mohamed-alaa7]

from Egypt big thanks

[@MichelvanBiezen]

You are welcome and welcome to the channel!

[@blackmamaessa]

Thank you soooooo much!!!!!!!!!!!!!!

[@biancarene2665]

is gauss-jordan elimination the same as gaussian elimination

[@MichelvanBiezen]

Yes, they are essentially the same. (they have different formats of representing the same technique)

[@nathanbonilla7440]

where is he getting the 9/3 from?

[@MichelvanBiezen]

3 = 3/1 = 3 x 3 / 1 x 3 = 9 / 3

[@johnbannister5046]

i have no idea why the 1 didnt change if you're multiplying it by -5/3

[@MichelvanBiezen]

+John Bannister Row 2 is multiplied by (-5/3) and then added to row 1.

[@wilsenmarchello8904]

Hello im from indonesia🇮🇩 Thankyouu for this vid

[@MichelvanBiezen]

Welcome to the channel

[@jonathanmachado1932]

bro went crazy 😂❤

[@MichelvanBiezen]

Glad you liked it. 🙂

[@angelicarincon1350]

thank you !!!!!!!!!!!!!!!!

[@arinaazyr6347]

tq sir

[@buddzfn2895]

Thank you so much! It took me a while to solve these types of equations.

[@MichelvanBiezen]

You're very welcome!

[@numbtiger9349]

Thank you

[@MichelvanBiezen]

You're welcome

[@Googlename699]

you are amazing

[@MalikUsman-xh7kx]

thank you

[@MichelvanBiezen]

You are welcome. 🙂

[@musagaming6639]

Thank you so much sir ..your are the great ....🥰

[@MichelvanBiezen]

So nice of you

[@salmofn]

THANK U

[@MichelvanBiezen]

You're welcome!

[@jackcreech]

this guy came in clutch

[@MichelvanBiezen]

Glad the video helped.

[@katlehokhoele5750]

you saved my life😭😭😭

[@MichelvanBiezen]

I wouldn't go that far, but we are glad our videos were helfpul. 🙂

[@Scott15405]

how come -10/3 +3 is -10/3 + 9/3 where did the 9 over 3 came????

[@MichelvanBiezen]

Andres, what is 9/3 equal to? This is just the mathematical trick, converting 3 to 9/3 in order to find the common denominator.

[@Scott15405]

Michel van Biezen oh now i've got it :P i forgot fractures,now as i reviewed them ,i understood :) And Thank you for this video !!! Now i am starting to understand Gauss. :)

[@KhalidTerkawi]

come on dude .. 9/3= 3 ... did not change ... just wrote it in diff way

[@khankakar5583]

Thanks👍

[@MichelvanBiezen]

Welcome 👍

[@rookthelion2178]

THANK YOU

[@MichelvanBiezen]

Glad it was helpful.

[@rookthelion2178]

@@MichelvanBiezen you have helped students around the world not just in your classroom ^.^

[@chocolateangel8743]

If you started out by subtracting the second row from the first row -- and put the result in the first row -- you could have avoided the fraction work.

[@MichelvanBiezen]

Yes, but that is not always apparent as you start such a problem.

[@chocolateangel8743]

@@MichelvanBiezen Yeah. It took me a good amount of practice to start seeing things like that, but I also think avoiding fractions was my motivation. 🤣

[@MichelvanBiezen]

It is a good practice.

[@Hunterboy0511]

3:18 where is he getting 9 over 3

[@MichelvanBiezen]

- (10/3) + 3 = - (10/3) + 9/3 since 3 = 9/3 We need the common denominator before we can add.

[@ThroatGoatLorax]

@@MichelvanBiezen but why 9...? could I have done 12/3?

[@ThroatGoatLorax]

nvm because that would equal 4, I got it!

[@huh9672]

I HOPE YOU NEVER FEEL SAD EVER

[@MichelvanBiezen]

That is a nice gesture, but life is full of challenges and sad moments are inevitable. It is learning to make it through these difficult times and come out happy and resilient, despite these hard moments in life, that makes us the person that we are.

[@irakuri9347]

💘💘💘💘💘💘

[@MichelvanBiezen]

Thank you

[@LegoYoda7225]

rip right ear phone

[@MichelvanBiezen]

Apologies...When we first started our KZbin educational channel, we had ABSOLUTELY NONE, ZERO experience in video making. We were math/physics not film-making majors. So we had absolutely zero clue about stereo sound. Fortunately we do have a learning curve. So our “less old” videos are in stereo. A viewer suggested..."for anyone with problems with mono audio, just plug the headphone jack half way in and it will make it stereo, remember to plug it back before, after this video or people around will be listening to your device too!"

[@AtlantisDrews]

So freaking confusing I don't see you u can't just use substitution

[@lilyallenandthediamonds1749]

u talk like gru haha

[@osama0915]

You, my friend, just saved me from great confusion.THANK YOU!!!!!!!

[@MichelvanBiezen]

Glad it helped! Thanks for sharing.

[@ruthmiranda2498]

It helped me a lot! Thank you!

[@MichelvanBiezen]

Glad it did.

[@anthonymoore3246]

Thank you!

[@MichelvanBiezen]

You are welcome. 🙂

[@huh9672]

THANK U

[@MichelvanBiezen]

Welcome 😊