Row Reducing a Matrix - Systems of Linear Equations - Part 2

[asdfgh1880]

Ur videos are awesome. Really good explanations. :)

[elyas2208]

15x15?? your crazy buddy!!

[BABYLiNxP]

I am so glad to have found your videos.. they have helped me a lot! thank you :)

[patrickJMT]

@BABYLiNxP glad i could help, come back any time ; )

[kdanladi]

Thx, man. You are very helpful

[mardi8000]

thanks man. really helped me while reviewing for my DFQ final. didn't know how to solve for eigenvectors lol. saved me LOL. keep up the great work!!

[XwP1ayawX]

15x15? I'd cry

[JoshuaWcoates]

thanks for making these videos patrick! your explanations make it seems so easy really... too bad my algebra professor can't explain it like this

[jabbasias]

thanks!! this video was rellay helpful!

[awanoor1]

thanks a lot for your helpful videos.

[ahmad65563]

thank u 

[purepinoii]

15 x 15 by hands ~ 

[masterchief9064]

awesome vid, really helped me a lot. about changing the order of the rows, are you allowed to change the order of the rows if you are trying to find the inverse of a matrix? i mean if the left hand side were the coefficients of x, y, z and the right hand side were the identity and you had to get the left hand side to become the identity? i know i probably didnt phrase that question very well, but hopefully you get what im trying to say. :D

[shabalabaist]

THANKS A LOT

[stridexr]

Thanks, had to write a computer program that would solve for x number of variables. This explained everything, you the man :))

[patrickJMT]

@stridexr glad to help. this stuff is painful to do by hand if you have a system that is at all large

[TheFallenH3ro]

Thanks I really appreciate the video I was confused as hell at first lol....you helped a lot and I got an exam 2morrow night

[patrickJMT]

@TheFallenH3ro good luck on the exam!

[varadakhot]

THAAAAANNNKK YOOUU! I got a bad prof for linear Algebra for first year engg.. Think I'll probably be visiting your site a lot over the next 3 months. In fact, your videos helped me lot through high school calculus too. I respect you a lot as a teacher. Thanks again!

[patrickJMT]

@varadakhot glad that i have been able to help you : )

[brawl313]

again, thanks a lot.. it was a bit hard to understand when explained without explanation but thanks to you, all it took was 15 minutes to understand it all XD

[Akineyle]

Nice vid! Keep posting! I love your way of teaching. Everything is nice explained.

Respect

Grtz from Belgium

[anukefromrussia]

You're awesome!

[HomebrewGuru]

--just memorization not understanding

[HomebrewGuru]

You gave a clear purpose and explained the reason behind each step clearly so that I can understand the concepts for what they are. Once I understand the concept and can use it easily then maybe learning shorthanded conventions or pet names for the concepts might save time, but throwing pet names and steps without a clear understanding of where things are going and why (not skipping steps and expecting students to catch it) makes material difficult to learn and master while encouraging--

[HomebrewGuru]

It's so stupid. Like I really don't care what an "augmented matrix" is or "pivot position" is and I don't need a detailed description of them. It really isn't useful for the book to come up with pet names for all of the concepts. I really don't care what they decide to call each step or if eliminating zeros at the bottom is called the "forward phase" and the top is called the "backward phase." I can't figure out where they are going with it and its an unnecessary introduction of jargon.

[HomebrewGuru]

It really isn't a complicated concept, even an elementary school kid can get it, but it is all about how the material is presented. Unfortunately material is presented in an inefficient manner at the college level under the guise of making the knowledge of the material "prestigious." It's the implied value through exclusivity principle at its finest.

[HomebrewGuru]

Thanks man you explained in 10 minutes a useful technique (a shortened notation for representing linear equations for manipulation) in what my book attempted to explain in literally 30 pages. There is a ton of balloonery/puffery in "terms" and useless jargon and conventions no doubt created by condescending mathematicians trying to make their stigma on society. The book includes steps and descriptions without giving any goal so I get lost trying to figure out where they're going with it

[patrickJMT]

@HomebrewGuru i am happy to help, but the rest of your comments are a bit silly, angry, naive , or all of the above. just because you do not understand does not mean someone is being 'condescending'. if this is your attitude about everything that confuses you, you have a lot of growing up to do still. try not to generalize a whole category of people next time. this is what racists, bigots, and political nut-jobs do. it is the reason half the world is screwed up and everyone hates each other.

[HomebrewGuru]

@patrickJMT

I'm not generalizing a whole category of people but it would be naive to suggest that the current state of how things are presented to college students is ideal (after all, why else would people be watching your videos if they could just read the textbook?)

[HomebrewGuru]

@patrickJMT

I mean, seriously, I learned the same thing in elementary school pre-algebra with systems of equations and how to find solutions to them and it was explained in less than two pages (or 10 minutes in your video) or explained briefly by the teacher on the chalkboard, why should explaining a shorthand notation take 30 pages? You gave a clear purpose and explained the reason behind each step clearly so that I can understand the concepts for what they are without unnecessary pet names.

[invisiblebutterfly6]

This is the first time I've been able to sit through a lesson on this without falling off my chair. Thanks for making a video that explains it so clearly! :D

BTW, how long did it take you to hand multiply 15x15 matrices ? :)

[zeeshanpolito]

Thanks a lot, help will be highly appreciated! :)

shani pakistan chakwal]

[PonyBoyJones]

@patrickJMT i just want to know what did you major in and what you do for a living. b/c i'm a pre-engineering major in my second year and i'm taking linear algebra as of now and i have no idea what i want to do after i finish. im smart but lazy at the same time... any solution? (i know you're not a guidance counselor lol)

[hawx786]

thank you again ur always a great help. and i have u to thank for my whole first year of uni for maths :) and i have to say ur great at teaching and make it pretty easy to understand these concepts.

[soldiermedic6140]

thanx for the help

[mmelkon0]

Thanks for the video but you have made it so complicated. just make the bottom triangle zeros and then solve it.

[TheFutureIsRightHere]

Could you please make a tutorial on how to do it on a graphing calculator?

[interxavierxxx]

Hi Patrick, I'm a little confused. What is the main difference between row-echelon form and reduced row-echelon form?

[emeraldmorn]

lol mine did not come out so nice. He is right about the ease of arithmatic errors. I have some nasty fractions solving the system on my own. gah! this is why I use my graphing calculator to solve these!

[mindbubble27]

saved by youtube. ah, thank you so much!! you're a great teacher. As opposed to certain overly complicated text books. :D

[satti199]

what is this method that you have used??

is GAUSS ELIMINATION , GAUSS JORDAN OR WHAT????

[mindbubble27]

@satti199

sorry, i don't know if this will still help you, but he used the gauss-jordan method.

[baby16gurl9]

hahaha i started this an hour ago wtf

[RiverKnight2]

you have saved me, my precalc teacher is amazing, but she gave us this assignment and didn't give us any instruction beforehand and i had no idea how to do this one problem about this. and now i do! thank you!

[MrSwiggity]

This video was a life saver. I'm learning this today and the way the teacher and book explain it, it makes no sense whatsoever. Linear algebra by Gilbert Strang fourth edition :/

[vivrey666]

...you're awesome!...keep it up 'kay!

[qariqasai]

thank you very much man.....It helped me alot as tomorrow is my paper...But, I still hate math....

[chtmtlmt]

using matrices to solve linear equations is so much easier to understand! In my textbook they don't use matrices and I really didn't get what they were doing but now I do. Thanks so much, great video!!

[kawaii22devil]

OMG!!! you are a life saver!!!!! Thank you :DDDD

[tweezybabeh]

I gotta test tomorrow, and you just saved my life!

[CorrectionPen]

Hey patrick, can you do a video on proving if a matrix is idempotent or symmetric?

and show some examples?

Thank you, you are very helpful.

[honglee87]

Hey Patrick,

Thanks for the great video.

I have a question though:

How do you solve a system of linear equations, when some of the rows is equal to zero, example,

50a-30b=3

-30a+70b-30c+d=0

-30b+80c-d=0

-b+c=0.5

So you see 2nd and 3rd row is equal to zero so the answer for b and c will be zero? How do you solve this?

Thanks.

[Sigut100]

zkurvená pičo



[patrickJMT]

@Sigut100 i have no idea what that means!

[delirman92]

@patrickJMT Better like this....Matrix won't help to translate this entrie. Seems some slovak buddy had a hard time reducing matrix....

[Mi28N]

@patrickJMT well.. he's telling you, that you're a fucking bitch.. I don't know why, he's probably retarded

[patrickJMT]

@Mi28N ha, that is why i love the internet

[aandgpointlessvideos]

@patrickJMT google translate....ahhhh

[Mi28N]

@Sigut100 seš idiot

[mex301]

Great job, keep it up...

didnt get it at all when my professor at my $33,500.00 school taught it to us...

but this video sure made since of it...

[tuestresfat]

can someone explain to me the idea of a matrix and why it works? I really appreciate this video explaining how to solve a system using matrices, replacing everything with 1's and 0's, but WHY does it work? Why are we able to simply divide an entire row by -1/28 and it doesn't alter the original question?

[tuestresfat]

when you say punch it in a calculator, you mean just the basic arithmetic? like 5*12 = 60, stuff like that? or were you referring to a different method with the calculator?

[s8715053122004]

large linear system in my life every day in my pants

[1966zaim]

@s8715053122004 

[Thevick94]

Thanks soo much !! i used to love math. Then it got complicated...way complicated !.

I think its b/c i didnt understand it, but you've made it so clear and simple!

Thanks so much, i love math again !! ~

[patrickJMT]

@Thevick94 well, it gets as complicated as one wants. glad my vid helped though!

[eliminator3]

@patrickJMT I was taught to get your REL form before starting your RREL form. These two videos proves to me that you can do RREL form from the start... that removes a LOT of extra work in the future, thank you for proving a shortcut to get the right answer. I know my professor simply wanted everyone to understand the format before continuing on, but this way, I can still do less work and still show all of my work, great vid!

[Rahath4]

Math 160! Lol

I took this class as a senior in High School.

It was hard, my first test was a disaster.

But once you get use to it, Matrix Algebra isn't so bad.

Thanks for the review Patrick! :D

[patrickJMT]

@Rahath4 you are very welcome!

[qwertyfshag]

i am not allowed to use a graphing calculator for my exams. it sucks. i need a calculator that does matrices without graphing capability

[gian2g]

This is cool man! Is this from Linear Algebra?

[BlueNightengale]

THANK YOU SO MUCH

i have a quiz over this tomorrow and i didn't understand it at all,

now i get it.

:D

p.s.- you should use a dry erase board or recycle all your paper, cuz that was a lot of paper >.<

p.p.s.- 15 by 15 matrices by hand...*shudder* thats a scary thought

[127hopest]

u are amazing....thank u soo much i ve have learnt soo much more using your videos than i have paying £3000+ a year at uni!!!!!

god bless you!!

[MyMindIsMyWill]

@patrickJMT hey can I kidnap you bring you to my house one day?? You are absolutely one of the best people at explaining math on this planet. I wish there were more math teachers like you who aren't Im sorry to say aren't very good at explaining stuff in math. If we had more people like you working in math our math scores in the U.S. would skyrocket. And I'm not joking...Thank You.

[Presidente7878]

I'm a heterosexual so I don't usually love men - well of course John Shaft - but I love you. You really saved me with these videos.

[c808boy]

dang, you must use up sharpies really fast haha

thank you so much for this!

[1mbilalk]

You the best math teacher , buddy , tutor what ever you say .. but your words really embeds into brain and helps a lot in exams or quizzes

thanks a lot patrickJMT

[twiggy6666]

What makes one of these problems inconsistent?

[jansta]

without a doubt, your videos helped me increase my math grade 2 letter grades.

Thank you!!

[weatherman700]

Great tutorial! You're saving my ass on an exam tomorrow (since our professor didn't explain this very well).

Thanks a bunch!

[abbyness8907]

will you be my personal tutor?

not joking at all.

[acquiesce022]

EXCELLENT TUTORIAL! You explain/ expatiate well and when tutoring any math/ science topic well, going a little in depth (which you did) is a good thing! So no, you didn't rush and covered this nicely.

[IDKWHOITWAS55]

So much work for simple answer.... WHYYY!

Looks like I may NOW have a chance on passing my test compared to just listening to my class lectures... :(

[lstiller1961]

Can you show us how to input data into TI-84 calculator to solve the matrix?

[littleflower717]

thanks so much,

this was extremely helpful ! :)

[lizcc33]

u were very helpful.

thanks

[karlkarlkarl1234]

How do you do an eigenvector? Is it much more complicated than this?

[VelociralexBojarzin]

My exam is this saturday, and it's a daunting three hours long. Should be fantastic.

[MrStarky1990]

@VelociralexBojarzin ouch exam on a saturday : 0

I swear this guy does my maths lectures word for word but in a quarter of the time, soooooo good

[asicaval]

Thanks a lot you guyz Rock!!

[deadlytux]

thanks for the simple but very nice explanation!

Here a Belgian student who thanks you!

(only, today exam...)

[lyaskoff]

Hey Patrick,

Once again, thanks for the great and very helpful video. I have a question though:

How do you solve a system of linear equations, when some of the rows have less variables, for example:

5x+y+3z+a=1

x+y+2z-2a=-1

x+y +2a=1

3x-y+z =4

So you see 1st and 2nd row have 4 variables, but 3rd and 4th have 3... How do you solve?

Thanks a lot, help will be highly appreciated! :)

[000itsjustme]

you just put a zero where that variable would be in the matrix

[EmuZimbak]

hey that;s the same thing as

5x+y+3z+a=1

x+y+2z-2a=-1

x+y+0z+2a=1

3x-y+z+0a=4

so in your matrix, for every variable that isn't technically written, you put in 0

[lyaskoff]

yea I managed to solve it :) thanks for pointing out!

[MIS0HAPPI]

for the missing variables you just put a 0

so the 3rd row would be

x+y+2a+0z=1

[ufo8mykat]

Excellent verbal instruction, thanks for demystifying. :)

[GoldXpert]

dude you are the best. Thank you very much

[OTorehnai]

hey patrick, i tried a different method using elimination by parts and i get different answers and substituted it to the equation and its correct! is that also possible? why is it different from you're answer? using row reducing matrix? x y z

(-31,16,5)

i thought it will be the same??

answer asap plss.. :D

[huntflex]

thanks very much for these vids, im a first year Electrical engineering student, had some difficulties in linear algebra, this helped me :D.. keep making such great vids!!

[liukolun]

OMG you made it so easy to understand!!! I hope I get a teacher like you lol.

[yadth]

I am in the home stretch in my college algebra class. We are currently doing matrices, determinants and inverse. This is what my final will be on. My tutor has showed me how to put the problems in my calculator, however I still have to show some work. Your video has helped me get more of an understanding. It is still confusing, and yes easy to get mixed up. Thanks!!!

[nyadon]

Thanks I never studied this in high-school "1971" or in college 1998, and 2008. You made it fairly simple. I feel I have the concept and hope I can tackle these as easily as you made it look.

[DJInfinity24]

awesome!! i thought i knew it already, but i had some confusion...this video sure helped...keep it up!

[tigernov6]

tedious* hmmm. Is that your favorite word? I have noticed you saying that word a lot.

[patrickJMT]

if i use the word 'hard' people do not try

[patrickJMT]

and a lot of math is tedious : )

[RyanSantiagoOnline]

What is the echelon form?

[cobreaper2]

An ''echelon form matrix'' is a matrix that obeys these 3 conditions :

1) Any row(s) of all zeros must be located under every non-zero rows;

2) The first non-zero element of every row must be a 1 (these 1s are called ''pivots'' since they are the first non-zero entries in the row);

3) The pivots (the 1s) must always be located at the right of the pivot in the preceding row.

[LOLUNIT]

lol, we have to do it by hand :(

[noVicda]

thx man I needed this 4 2morrows final

[SrFabio]

Man this is great, it's far better than regular class explanations lol keep it going ;)

[BigDaNNyBoi1989]

15 x 15 matrix multiplication BY HAND - thats crazy! lol

[Isomnophilia]

You voice and words and examples makes this a pleasure to watch, gonna check out the rest of ur vids!

[acerza89]

thanks bruv

[LeviJean99]

you are a saint, seriously. thank you so much for this tutorial, it helped tremendously.

[patrickJMT]

happy to help : )

[Sajiv9]

This is exactly what my prof is teaching. Thanks for the help. Are you a U of T student?

[patrickJMT]

nope, my student days are over!

[saintseiye]

thank you!

[shinakuma9]

Helped me understand my assignment before the midterm, thanks :)

[xxrobby]

University of Toronto?

[KYPproductions]

Downtown or Scarborough?

[XXSAD]

Thanx a lot

[scientistogbondus]

fabulous

[sparrowax]

hurray! i was contemplating suicide but now i understand it and i am going to ace my homework thank you thank you thank you!

[patrickJMT]

i hope it was not all that bad!

[the12packweb]

This seems, to me, to be very similar to simplex algorithms, but without inequalities or maximum targets. Your finding out the separate variables instead of the potential best outcome of the combined variables. Like working backwards? Never seen this method before, Interesting thought. You say this is undergraduate material?

[patrickJMT]

high school material

[the12packweb]

I was going to say, good tutorial anyway.

[ronburgundy28]

you are my saviour. thankyou!

[patrickJMT]

you need to frame a picture of me with some candles somewhere in your home!

[katiep87]

this was a huge help, you're so much better at explaining then my prof, thanks!

[naruto95823]

thank you =)

[pacitama]

I start Finite Math this September, and the teacher gave us homework to start before getting into the class! Your Linear Equations, and Reducing Matrix video's were a huge help and cleared up so many questions.

Thank You!

[phantomx2003]

It's funny, you ever watch or listen to something and said to yourself you'll never understand it.. but then it just pops in your head like "hey I think I understand how that works", and you get a stupid grin on your face??

Lol *grins*

5 stars

[patrickJMT]

sweet! i am glad that you now understand! give it all a bit of time, and you can understand anything

[rakista4hire]

are you using gaussian elimination?

[patrickJMT]

yes, that is another name for this procedure i believe!

[rakista4hire]

ow good thing you're always online!!

mathematics is really hard.. especially this matrix algebra.. but you're integration tutorials really helped me in integral.. thanx a lot

[patrickJMT]

ha, i am ALWAYS in internet limbo waiting!

[clansman89]

Thank you!!

very helpful and it's way more interesting than just learning from the book :DDD

[bbddbdbd]

Please post up Descartes Law of Signs next I don't get that either! Thanks

[sheshd]

legend!!!!

[sauljoffe]

who needs to go to class when you can learn it on youtube in your own comfort!

you are a life saving genious,

keep posting these amazing videos

[MetalManiac257]

Cheers, you saved me reading some boring text.

[raachaell]

wow 15x15 would be rather time consuming!

When you divide a row by an integer, do you bring that number infront of the matrix so that it is multiplied be it or something? I don't know why I think this but I'm confused now....

[mitmfan]

I hope you don't mind me answering it, since I know the answer.

The integer you divide by (in the example he provided, -28) simply drops out. For example, if you have 7x = 35, you divide by 7 on both sides of the eqaual signs. The 7 you divided by simply drops out leaving you with x = 5. The line he draws is like the matrix version of an equals sign. Just like the 7 in the equation dropped out, the -28 in the matrix dropped out.

I hope that made sense to you.

[raachaell]

Yeah thanks! I know where I was getting confused now - you can use row reduction to partially reduce a particularly large matrix to make the dterminant easier to obtain, then you need to keep the integer for muliplication at the end. Thanks :-)

[alsaceda09]

thank you so much its really really helpful and i understand it now xD

[DaniD520]

Very helpful. Thanks so much!

[GearGOD]

Thanks a lot for taking the time to explain this stuff on video. Very helpful.