Row Reducing a Matrix - Systems of Linear Equations - Part 1

[PUNKFUSION1992]

how do you do homogenous linear equations?

[aerialaces21]

After using your video's for so long Patrick i now watch these immediately after the lectures instead of waiting for the night before the exam. I have to say it has made this semester a lot more smooth than usual!

Thank you!!!!!!

[patrickJMT]

@aerialaces21 yes, i found out the same thing! reading a section before we went over it in class helped me tons

[BallpenEater]

Good day! Is it necessary to change the rows? At our school, we weren't introduced to that technique.

[6BURG9]

@bikeous23

You're in pre calc... What kinds of systems are you solving? 2, 3, MAYBE 4 equations? Try using substitution and elimination on a big ol' 6x7 system without Gaussian elimination and tell me your way is faster and with less margin for error.

[6BURG9]

Ugh is it just me or is Calculus actually more fun than LA? Getting the hang of it though thanks Patrick!

[1218el]

tnx.. i learn a lot more power man..

[impotentarab]

if you don't mind answering, where did you learn maths patrick?

[patrickJMT]

@impotentarab school, books, my own. the normal places i think.

[jaker0135]

Thanks for the video. I couldnt figure out how to solve using this method but after watching your video I figured it out. just in time for my final exam tomorrow. Thanks!

[patrickJMT]

@jaker0135 good luck on the final :)

[elleen54]

what if you don't get 1 for the second number on the second row? what would you do?

[carolina27941]

@elleen54 you have to make it a one or else the end results are correct

[meers93]

thank you so much for this!!

[Killuminatismd]

omg....this is beautiful. He explains it so perfectly. gotta love PAT!

[purepinoii]

omg yes thanks!

[TheLoveformankind]

I LOVE U !!!!

[yukun92]

I have stopped listening to my calc professor and began relying on your videos. I don't know if that is a good or bad thing. I am, however, getting A's on my quizzes since I began to listen to you, so I'll take it as a good sign haha.

[patrickJMT]

@yukun92 ha, watch videos AND pay attention in class : )

[lolkiwi]

guh... I liked calculus better. Never thought I'd say this!

Thank you :)

[ramroomi1]

Thanks very helpful!

[baturinj]

It was good, thx! (:

[YamiThunderous]

Although this technique is great, it's really slow compared to calculator. xD

[patrickJMT]

@YamiThunderous an abacus is even faster

[Basram]

I've never seen this done before. What a great system! I don't know if my teacher would like me learn it though :)

[patrickJMT]

@Basram i think your teacher would be fine with you learning. ; )

[UnleashedFire]

PatrickJMT, your videos are useful for learning the basic, I face all kinds of complicated exercices in my book.

[patrickJMT]

@UnleashedFire go forth and apply

[Light3282]

thank u ! i was struggling with this !

[mierty21]

but what if oyu don't have a one in one of these equations?

[tetrawavern]

Perfect explanation mate. Thank you so much. This cleared up my lecturer's messy notes! Great video. Helped out a lot.

[Ombaeh]

Next Lesson...Encouraging Suicide before we start with linear systems

[KavishTanna]

Kahn Academy doesn't have sh*t on this! Keep up the good work!

[SuperPowderkeg]

Thanx Pat, you bypass all the shit and keep the important things clear! You've really helped me out! keep em' coming!!

[iamtheasianjamesbond]

omg patrick, i need you for eigenvectors LOL

[cuilboy001]

how to know what equation to use because i always use the wrong one



[bikeous23]

This is the most inefficient way to solve a system of equations. It takes way too much time and there is huge room for error. Isn't mathematics about solving the problem the quickest and easiest way?

[patrickJMT]

@bikeous23 i am not sure how to respond. you just seem a bit angry about it all. this is a wonderful way to solve large systems of equations. what method do you have that is more efficient?

and what does: there is huge room for error? there is no room for error if one can do arithmetic correctly. yes, there are lots of computations, but we are not adding 2 + 2 here...

and no, math is not as trivial as you seem to make it.

[kakikukimakko]

@patrickJMT cool..in your face bike

[kakikukimakko]

@patrickJMT  cool..in your face bike

[Abhishhehehe]

@patrickJMT i think he means for solving the system of equations where u cud just multiply by two and subract the equation 1 from another ..stuff gets cancled out and u can solve it...

he is missing the point of the video which is learning row reduction. so his comment is just stupid.

[Newdiabetic]

@bikeous23 Patrick has done it in the simplest way possible, at least by what I have watched. Have you taken Linear algebra or are you just spouting nonsense?

[patrickJMT]

@Newdiabetic nonsense is the norm of the internet (and of the world in general)

[bikeous23]

@Newdiabetic I'm in Pre-calculus, its easy to understand how he does it but its too time consuming. Too much room for error that's all. It can be seen as comparing two computer programs that do the same thing but are written differently. The better program would be the faster one, get what I'm saying?

[kaflavik101]

@bikeous23 Surely there are much simpler ways to solves systems in 2 or 3 uknowns. But the method introduced in the video can be applied to any system in x number of unknowns, which is the real stregth of the method.

[Palmgren86]

@bikeous23 If you're lazy you can use software like mathematica or maple.... that shortens it down to one command like gausselim, or gaussjordan or something similar, but you still have to define the system.

Thanx from Norway for the vids.

[jazzysax102391]

@bikeous23 I have to disagree, whilst solving systems of equations involving many variables this is the best way. You will find that using this method with Partial fraction decomposition, when you can get 10 or more variables for very complex equations, matrices are undoubtedly the easiest and most efficient way, especially considering all it takes is very basic arithmetic.

[finnvoid]

@bikeous23 for a few equations with few variables the time it takes isn't quite efficient, but the power of this method is more obvious when you're dealing with MANY equations and/or MANY variables, which are more likely to occur in real-world applications

[josepm00]

Hey man, thanks for everything. I got to the university of waterloo.

I can certainly say that you are better than everysingle math teached I have ever had.

[SpaceBandit666]

I can see how people would be very confused, you shorten your steps rather than showing your work. For example at 6:50 your doing 2 steps at one but not showing anyone what your really doing (I got lost a few times). This video helped clarify some things that I had trouble understanding thank you for posting this video

[patrickJMT]

@SpaceBandit666 if i wrote out every single arithmetic step, this video would take about 10 years to make. you need to be able to fill in some stuff as you go. there is a pause button. try to fill in the steps yourself and you will actually start learning.

[her008605]

@rolle16. Please note the formatting problems in my note. The formatting should be:

4a + 5b = 12

-7a + 2b = 18

[her008605]

@rolle16. I'm not Patrick, but I am a math teacher. The values he chose do not have to be those exact numbers. The goal is to convert the coefficients of the matching variables such that when you add them, their sum is zero and they can be eliminated. Example: 4a + 5b = 12 -7a + 2b = 18. Multiply first row by 7 and second row by 4, then add. The a variable drops off in each row, allowing you to solve for b.

[rolle16]

sir, this is an excellent vid but may i ask you a question? what i dont understand is for example at 8:32 you say that you take -2R2+ R1 and 5R2 + R3. how do you know that you have to chose that? Is there a way how you can see this? (sorry for my bad english)

[emeraldmorn]

@rolle16 which rows you choose to multiply by and add to other rows is entirely up to you. there is no one "right" way to reduce a matrix. some paths may be faster than others, but sometimes even that is impossible to tell in advance. IOW use your good judgement and then don't sweat it after that

[gerardaddict]

Is this the Gauss-Jordan Elimination?

[TheTalmon18]

by substition of course

[TheTalmon18]

Patrick, the problems i get, i get the zeros first

then when i try getting a 1, i get the 1 but then the 0's turn to different numbers

I dont know how to make that a 1 while keeping the first 0

so i just get all 0's and one number in 1 row, then solve the others>.>

[Daltex951]

can you do more examples of this

[patrickJMT]

@Daltex951 there should be quite a few of these if you search for them on my channel page

[XxiPodxX1]

WOW you have no idea how much this helped on my finals yesterday THANKS ALOT!!!!

[Mike01010011]

thanks

[carpevlog]

You are honestly amazing. I have been trying to figure this out by myself for FOREVER, and I watch this once- AND COMPLETELY UNDERSTAND IT. You are brilliant.

[Bluelincolnpark]

THANKYOU!!!!!!!!!

[dagosto11211]

Just want to say thanks alot for posting this I didnt understand it but now I do =D hopefully I get a good grade on my test but I can see you a gifted at math thanks again =D

[xxxcartooonxgurlxxx]

do we have to switch the rows? or can be just solve it the way it is??

[cod4lover123321123]

ok i got every part except the part how i stop a bullet or doge them??????????

[hckynck20]

Thanks so much for these videos! I pay thousands of dollars for college math courses and just get confused by the teachers, then i watch your videos and it all makes sense! keep up the good work this helps a lot!!

[joeldsouza2]

i think you could plug numbers in x and y to find the answers right

[DenDhur]

You explain things in an excellent way! thanks to you I finally got a hang of matrices´;)

So thanks alot Sir!

[moveest]

Its simple like 1+2

[qwertyfshag]

you are the best

[Q8RedDevil91]

how many emails do you get per day ???

[fairygool]

matrices is still really difficult for me , especcialy the 3 by 3! I understand when you explain it but on the exam....... wow noot alll all. all this switching and adding and changing... i get really lost

[patrickJMT]

@fairygool matrices can be pretty confusing - there is just so much arithmetic and book keeping to do. all we can do is keep practicing! it will come to you!

[fairygool]

@patrickJMT i'll try... :D

[1991hayla]

@fairygool

yea the same to me;(

i am afraite that i will not pass from math;(exam

[TheFluxProductions]

@fairygool buy brains on ebay 99usd each!

[randomlego55]

this is very amazing and i understand everthing here

GREAT JOB BTW!

[jazzysax102391]

I have just finished AP Calculus and gotten a 5 on the exam, and I have never learned this : (

[fcortinahernandez]

Excuse me. You don't know anything about History of Maths. This is the Gauss-Jordan method

[D3vilPri3st]

this video is so great,i have my final exam tmr and now i understand this crazy calculation,thanks.

[fateater77777]

Are you a wizard?

[pdg5333]

You saved my ass at least a dozen times in highschool, and now here I am a junior in college and you bail me out again. You are a freakin math god sir

[patrickJMT]

@pdg5333 ha - that is awesome for me to hear.

if and when i make it to the pearly gates, at least they will not accuse me of being totally useless in this world.

[TheBucksB]

no no no, i was looking for upper triangular matrix video...looks like i came to the wrong place

[kylemartin3]

Thanks! My engineering professor decided to throw this and a bit more material at us yesterday. You made it easy. :)

[ficovozicico]

wow.. this stuff just takes too little credit... honestly man.. well done

[Inaneen]

you're a life saver! Thank you

[bianco0727]

Dude u r a genius. Thanks buddy, u rule!!.

[14s200]

really nice video, thank you..

[karlkarlkarl1234]

That 2 looked exactly like z, had me confused for about 5 minutes :P

[yaamo]

The only way u will understand it is if u constantly pause and rewind it, I know that's what's helping me! But at least unlike ur prof. u can pause him and repeat him! Good Luck!

[PLGodly]

@ Beasal007

how old are you??

[valeagrl1]

rewind play - rewind play - rewind play LOL

[theenigmaticone818]

WOW, thank you, my book does not show how to do the matix method i thank you that you posted this up, i was a bit confused but your example is really clear and organized. THANKS

[jeevanrokz]

mr patrick ur a best teacher....i'm a student in india

[BigHunger]

at 7:31 when you mention you want to make the entry in the middle a one, why didnt you just divide the line by -5? so you can end up with a 1 in the middle instead of switching rows.

[aafrophone]

i think he was trying to avoid making the rest of the row into fractions

[trassssss]

what if all of the x's are not equal to 1?

[EdikShepherd]

Oh man, my brain just had a seizure. I'm only in 10th grade Geometry, I have no idea what this is!

[caterpie787]

Really? This is in 9th grade algebra :D

[jwt3213]

His examples might be in 9th grade algebra but the method applies to much more complicated systems of equations. Plus getting used to solving them in matrices is nice because once you get the idea behind how it's done then you can learn how to find the inverse matrix(of the left side) on a calculator and multiply by the right side to get the answers of very complex systems in a matter of seconds.

[marekgola]

Dude, I have a chinese teacher and i was frreaken out cuz i didnt understand shit. Now it seems very simple. Thank a lot!

[javflo2204]

hahaha i have a chineese algebra teacher and its really hard to understand what he says, and his jokes he tells in class are so weird and random... i tried to change out of his class but... they didnt let me... lol

[sqeeekboarder]

Lol i'm part of the 'chinese teacher' club too... any chance you guys go to UVU? lol and thanks for the vid, btw, i didn't know there was a test until today, and i didn't study, and my book is on the other side of the lake, in a locked school... Today is one of those days where you wake up and say "SHIT!"

[OTorehnai]

thanks patrick this helped alot! =)

[30x60]

is this somewhat similar to gaussian elimination??

[cobreaper2]

Yes. This method is called Gauss-Jordan elimination and it's a specific kind of gaussian elimination... it's much longer, but you get the result directly...

[Thundermand]

Yes, it is.

[vampySARAH]

man this COMPLICATED !!!! who ever invented this is CRAZY ...!!

[patrickJMT]

yes, it is very tedious : )

it is 'elimination by addition' with only the coefficients in the matrix.

this stuff is super super useful though in many applications!!!

[tessabug101]

Oh my gosh, thank you so much for this video!  Last year in my Algebra class I learned systems of linear equations, and I need to do an Algebra review of that this year in Geometry. I really needed that help, thanks again!

[jse07]

can someone explain something to a laymen

at 03:55 you state, "negative four times by zero and add 1 that will just give me one" how does this make sense?

-4 x 0 = -4

-4 + 1 = -3

i take it im totally missing something here but i dont see what

[himynameisakshay]

Jse07,

-4 x 0 = 0 due to the multiplicative property of zero.

0 + 1 = 1

[ginasexy78]

-4 x 0 = 0

ANY number times zero equals zero

[AlessiChristimatrix]

dude. -4 x 0 = ZERO thus, 0+1=1

[patrickJMT]

ya, no problem : )

go forth and spread the math gospel

[technolifevlc]

@patrickJMT

die die die die die

[dragonxd1124]

scampern u do the same u would still multiply them remember the rules of adding negative

[Scampern]

What do I do if I have a column matrix that should be equal a column matrix?

bo=(y1/8+y2/8+y3/8 too y/8)

b1=(same here, but y's have -+ signs)

b2=(same as above)

b3=(same as above)

The plusses and negatives on the y values are different in each, but add up to 4 negatives and 4 positives on each row of the column vector.

I dont expect you do solve it, but how do I start?

[RapidFireAlgorithm]

Oh man.....Gaussian Elimination....try doing this as a fortran program with Gauss-Jordan Elimination and Gauss-Seidel.

o.O

actually, you're method is way more clear than the way I was taught. My lecturer made things so complicated.

[patrickJMT]

nice, fortran!!!

[alrightypewriter]

You make it look so easy but I know on my own I have the hardest time coming up with how to deal with the rows. Cramer's rule is so much easier but my professor doesn't want us to only rely on Cramer. :-(

[EdgeStormcrow]

matricies are powerful, this simple system of line comparisons can be abstracted to special cases of almost anything that you can think of. Primrarily spacial freedoms.

[EdgeStormcrow]

im doing university maths... no calculators for 3 years.. no calcs in tests or practice they say.

[Penfish2k]

most advanced math doesnt require a calculator.

[emeraldmorn]

@Penfish2k LOL except that I usually use a calculator to reduce matrices and have done PLENTY of advanced math. I just have to relearn it now to take the MFT and graduate with a math degree loll

[sakuranohana89]

you're calling -28 a big number?it's not that big , trust me, I've worked with bigger. Great technique btw,I'll use it from now on. I learned it a bit differently in high school I wonder if my college teacher will approve of this technique( I wonder if they even know about it)

[j1nj0]

haha priceless "i've worked with bigger"

[patrickJMT]

lol!

my wife is a teacher, and it seems that she was also taking about matrices one day in class... and was discussing the size of a matrix when she said: 'listen guys, i hate to break it to you, but size matters. it really, really does. bigger is harder usually.' or something like that!

she was quoted in the school paper or somewhere for it...

priceless.

[x0randomness0x]

LOL

[khair6006]

lmao

its a really good tutorial, helped me alot.

thank you :)

[SsSaNdRiNe]

I love your technique! You saved my ass in calculus. Thank you so much!

[patrickJMT]

ha! glad it helps.

[sparrowax]

you have opened my eyes! I finally understand!

[RicardoR5]

OMG i was looking at matrix movies and ended up here, got to love utube.

Has this over algebra (algebra linear in portuguese)in the school days, miss the old times :D

[filipemtx]

me too!

[flashback1234]

man this is way be on my knowledge!! Where do you use this for? Programming? Because I wanna get into programming so I might need it.

[sasuke305QB]

wow dud very nice, i learned it by the second problem u did, its amazing thx man now i know how to do linear equations =D

[tziady]

Excellent job explaining that... you rock man!

[sukit]

thnx man..u save my midterm

[evanester]

this can be done in a calculator

[patrickJMT]

any monkey can be trained to push buttons

[evanester]

so can any human...?

[Jaime44244]

how?

[colonelmatterson]

I just got my linear algebra textbook today for my math course this quarter and I was horrified to see it's full of matrices. I haven't seen those things since high school... thanks for the refresher!

[patrickJMT]

matrices are great! the basic ideas that matrices deal with are core ideas that get used in higher math! they are super super useful and good to understand!!

[muskanSETHI]

Thankyou so much ... u provided me with all the necessary help... thanks again

[patrickJMT]

no problem!

[phantomx2003]

Looks amazing. I have not clue on how to do it myself but I imagine if I knew all the rules in solving them and a brain the size of texas, I could do it :)

cool stuff!

[timmytrip]

very nice video :)has interested me :) lots cheerz 4 da post 5 stars and i have subscribed :D

[bbddbdbd]

your 2 looks like a z lol confused me

[patrickJMT]

sorry! : )

[mastergsan]

Good video, the only issue is that you always start with a 1 at the top left of the matrix, most of us are not so fortunate.

[patrickJMT]

this video is finished in another part if you are interested

[orangeblueandlavenda]

neato

[patrickJMT]

Hey! at 1:35, i said there is no solution if there is a number on the left side, but no number on the right! That is wrong! I should have said: there is no solution if there is no number on the left of the bar, but there is a number in that row on the right side. For examples, that would mean 0x + 0y + 0z =10 which has no solution! SOrry for the confusion... I just woke up and did not have my coffee yet!! : )