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

[@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.

[@Honest-King]

Wow I just had to scroll through the comments huh ?

[@kapto2636]

Wow that must be very funny to a group of children...

[@ninjahunterx7497]

Lol, that's funny. Hope she didn't get too many quotes for that.

[@TheGameconomist]

I watched your vids through tric, calc1, and calc2, now I am watching them in Linear Algebra

[@TheMarriumB]

sameeeeeeeeee

[@926Noor]

amen

[@zakusa9891]

what so you didnt know know how to do this while taking calculus. why is this in the pre calculus book then

[@stayingshredded]

Same here!

[@fkncompton7124]

Zak Usa you don’t use this in calculus. You use it in linear algebra which comes after calculus

[@jromdazy]

Genius! they say" If you can not explain complicated things the simple way - you have no idea what you are doing!" you definitely DO HAVE an idea of what you are doing! thank you very much!!!!

[@hexrx]

As a tutor at my college I recommend you to every single student who comes to me. You help in more ways than one Patrick. Thank you!

[@twothirdsostrich]

Holy crap. You explained this better than my professor did in an hour. Thank you! This will come in handy for my final this week :)

[@uesgaroe8998]

twothirdsostrich me too my friend...id joined in engg grad school and not even my prof was able to help me understand!

[@initiald975]

@@uesgaroe8998 I absolutely get it, I'm now in mech e, and numerical methods is giving us assignments with this straight out of the gate, ask us to work it out (and I said Idk what you talking about and ended up here) and we haven't even got to the second day of calculus 4 in the beginning of second semester. (numerical methods teacher said we would be learning things ahead of time, but dang!)

[@ToxicBullet95]

Patrick, I used to watch your videos since 2013 when I was an undergrad student, now I'm back again in 2023 watching your videos as a grad student. Thank you so much for your vidoes they have been really helpful in my journey. Whenever I come back to your videos I feel like I'm meeting an old friend where we got busy with our lives but I can't help it to come back here from now to then. I wish you all the best Patrick.

[@47Apple47]

It's amazing. My teacher teaches me for an hour and a half and I don't understand what she is talking about but when I get home and watch these videos, I learn a class worth of things un as little as 10 - 20 minutes. Thanks.

[@mytwohands]

After being out of math classes since May, I was starting to miss gold ole PatrickJMT. Glad to be back! Thanks for the refresher for Linear Algebra.

[@qiqalwana7283]

13 years later and your videos are still helping us, thank you.

[@instaminox]

who is doing it 10000000 tIMES and still getting it wrong xD

[@RS-gq5ws]

ihonestytruthful me

[@instaminox]

Shine Bright Like a Diamond focus well bro! it takes time but then it gets very easy!! and it will be a core for this course. plus learn very well all you can now. chapter 4 vector spaces is not cool because it's abstract and it connects all the mechanisms you are learning. stick to it and you will do well. good luck

[@pratisthakansakar6509]

ihonestytruthful me

[@ashishroy1781]

It requires practice to analyse numbers to simplify it properly. Practice at least 💯 proper problems of this kind, gain mastery in each problem, such that if anyone asks you any problem from that 100 problems, you can do that immediately; and then say your comment

[@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!!

[@DemiDemiGlace]

Never knew there were 10mins time limit in 2008

[@derrickampire]

Neither did I 😂😂

[@Dina-he1uc]

me neither! i was alwyas so confused watching his videos, wondering why he keeps mentioning he is gonna run out of time. Now it makes sense lol

[@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!!

[@thecardtrickstudent3870]

Thank you for making videos like this one right here without caring about the papers you waste in teaching us. Really admire it.

[@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!!!!!!

[@SmilerBFC]

You got me into university and now im beggining to work towards an engineering degree. I passed the first year now three more to go. Before i found the videos i had a D in GCSE maths. Not a clue on how to even expand brackets. My first thought was this... (A+B).... ( A+B ) :). Its time they played these videos in the universities replacing the lecturers. The simple fact is students would learn MUCH more! At the moment around 80% of us are learning nothing from your lectures.

[@patrickjmt]

well, if all the data points actually fall on a line, you can just use the equation to find a line y2-y1=m(x2-x1). If you have points that follow a trend but do not all fall on a line, you can find a linear regression. Conveniently, linear regressions are the videos i most recently made so you may check there.

[@aveiolofijazzy2248]

you sir are a beautiful human being who have changed the lives of many young engineering majors! thank mate

[@MS-ow7on]

THANK YOU!!!! i have a test in 3 hours... and i NOW understand this within the 10 minutes you taught it better than i ever understood it within the week my professor has tried to explain this!

[@ERAKONZ90]

You just saved my life rn cause I slept through one of my lectures and missed this. Thanks so much!

[@williamhorn411]

Nice having another left-handed brother. Stay strong soldier.

[@patrickjmt]

happy to help :) and it is a subject that tends to get more difficult for all of us. do not be discouraged; it is just the nature of the subject!

[@JessDuey]

As always sir, you're videos explained in 10 minutes what a floundering instructor attempted in two hours. Some day buddy, we'll all repay the debt we owe you.

[@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.

[@skagaser]

I can't thank you enough! I was sick the day we learned this in class and you have helped me tremendously!

[@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

[@ShannonLeighMusic]

Thank you sooo much!! This video was extremely helpful! My math teacher doesn't explain this like you did!

[@knoz35]

god bless you m8. my teacher couldnt explain over 15 hours all these. thanks a lot.

[@patrickjmt]

@cheechiongfun yes, you can swap rows - they are still the same equations!

[@Killuminatismd]

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

[@XxiPodxX1]

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

[@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!

[@010beachbabe]

i wanted to cry after leaving my math class the other day, but this helped me so much!! thank you. i wish YOU were my profesor

[@moek6200]

I'm literally watching this video in class while my prof has been trying to explain this for 2 hours lmaoo

[@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.

[@shivani2043]

Patrick you are awesome if possible i would have shown your videos to my school teachers and tell them that's how you teach.. FEEL LUCKY TO HAVE YOU.

[@Voltaic_Zephyr]

"IS MATHS FROM 2006 REALLY HELPING???" lol

[@David-wt5hf]

To answer your question, no.

[@dodi453]

you are a gift from the math gods.

[@D3vilPri3st]

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

[@KavishTanna]

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

[@tes_slamjam]

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!

[@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!! : )

[@598133]

life saver!!! math final is tomorrow. Thank you Patrick!!

[@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

[@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.

[@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!

[@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.

[@magaliebravo6679]

i love you Patric!! you have saved my butt so many times! thank you for all your help.

[@sidhantkumarsuar9150]

Hi Patrick, you are just simply amazing, tbh one of your examples in Calculus showed up on my IB Maths paper 3. You just make things simple but what I wanted to tell you is that in this augmented matrix, but I have a more efficient method for these augmented matrices although we will end up with the same answer but I guess mine will be a bit quicker. Anyways you were the one that changed my perception about maths.

[@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.

[@booksforcadence]

not me watching this in 2022 and getting confused that there was once a 10 minute limit on youtube videos

[@patrickjmt]

just spread the word about the videos and i will be happy :)

[@vampySARAH]

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

[@ernstblignaut3089]

thanks a lot man you safed my exams , you rule !!!!!!!

[@jmw1982blue]

Congratulations on 1M subs!!!

[@patrickjmt]

thanks :) i can't believe the channel has grown this much

[@amorag59]

Thank you for this, helped a lot for my test in.. 58 minutes :]

[@MythicBricks]

How did your test go lol

[@tetrawavern]

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

[@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!!!

[@notsohopelessromantic]

You've probably heard this many times already, but I wanna say it anyway- thanks! Younsaved me

[@zombiedude347]

Basically what these row reductions are is Multiplying both sides of the matrix by another invertible matrix. Basically all of the basic row operations are some of the simple invertible cases, when combined can create all invertible matrices.

[@Mesterie]

You are amazing

[@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!

[@TamerZiady]

Excellent job explaining that... you rock man!

[@jetswhiteout961]

How do you know if you need to interchange 2 rows, or use the other formulas you provided in the first step?

[@jazioxgaming]

BRO I'M OLD NOW!!! This man really said 10min time limit 😭. I remember those days!

[@Sleaslug]

the way you write numbers is like perfect to me

[@josphine291]

Hello JMT. You helped me pass calculus last semester. Thanks alot! Can you start uploading more linear algebra videos please?

[@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.

[@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!

[@patrickjmt]

@UnleashedFire go forth and apply

[@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!

[@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

[@patrickjmt]

no problem!

[@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

[@SsSaNdRiNe]

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

[@tsuratz]

so, how does it feel to write wirh left hand

[@Cowboys2SB]

Patrick, I'm not sure if there is a heaven or hell, but if there is, you are surely going to heaven first class.

[@stefanmitchell6877]

your videos are always helpful ,,, keep up the good work

[@mvpvic2407]

Thank you so much for this video! Great way of explaining the procedure by the way...

[@patrickjmt]

this video is finished in another part if you are interested

[@كيانريماس-ح1ض]

Your explanation is very simple and easy, I've really helped me thank + I'm from KSA =) ✌ ♡.شكرا من جد وربي شرحك جميل .

[@B.H.1987]

هههه طيب الولد مايعرف عربي بس جد شرحه واضح واحب فيديوهاته

[@patrickjmt]

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

[@maha_13]

you are an amazing teacher

[@manuelaidos]

i dont know if people will see this video but i will leave a comment well i want to say i know a trick a very useful one that my teacher said to solve matrices. The trick is when i want to modify a line below the pivot line what i do is L'2 (means the new Line 2) = L2 - ( L2 / L1) x L1 . This trick always works no matter wich line

[@Swanky723]

screw all haters in the future i am going to buy this guy something worth his input....$$$$$$$$

[@treehilllovin]

Thank you so much for all of the help!

[@marrytesfu3163]

you are the best Patric!

[@MDALAM-ki2fy]

thank you it's really useful. you made the understand this topic

[@MDALAM-ki2fy]

you made me understand this topic

[@BallpenEater]

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

[@valentinakhan1512]

sir can u please tell me that if i want to learn calculus from beggining then which calculus playlist should i watch atfirst . there are so many playlists of calculus but what is the sequence of the clculus playlists

[@comedian2479]

Question, for these procedures we don't want any fraction? The row 2 had [053] I instinctively would have divided row 2 by 1/5 to get row2×column2 as 1. Please respond back quickly, need feedbacks.

[@abdullrhmanalshehri4675]

huge thank for saving my grades

[@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 :)

[@sparrowax]

you have opened my eyes! I finally understand!

[@misssweethearted]

Thank you, you have such amazing videos and very good at explaining!! muaaaah

[@lya95]

Hi Patrick, what if I'm trying to find the m and b values? For instance, I'm actually trying to generate a model based on data points given to me. I'm trying to create a linear function that fits the data...

[@nicholasbraud1986]

can you multiply two rows by different constants, and then add them, say if its 3 and 4, can u multiply one by -3and one by 4 then add them?

[@JoseGarcia-tm9vr]

would it be wrong if I wrote R1- 4R2 --> R1? or do I have to write it the way you wrote it -4R2 + R1--R1?

[@TheVintageCurls]

thanks for the vid but what do you do when the first row, first column number is not 1?

[@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?