Homogeneous Systems of Linear Equations - Trivial and Nontrivial Solutions, Part 1

[@erikolson5672]

Patrick, I always recommend people to watch your videos. Your videos carried me through calculus and linear algebra. You are one of the few people who can explain any subject crystal clear. Thanks.

[@mugishachrispin1765]

how are you doing in life now I am taking the exact same classes

[@arwaa9861]

almost ten years and still watching this video,. thanks, Patrick!

[@tayyabzain6317]

almost ten years and math is still a pain in the ass

[@MiguelGonzalez-kp7hq]

I love yo so much. You save me in literally every class

[@Dan-bg5fm]

literally or figuratively ?

[@tordurhansen333]

I assume figuratively. I don't believe all his classes are math.

[@Dan-bg5fm]

Tordur Hansen lol i know

[@samratalha.]

Why do you LOVE him mann?

[@MorvyJ]

As with the other commenters, these videos are definitely coming at a good time. I've been following your channel for the past few years since calc1, and now I'm getting into differential equations and linear algebra. It is entertaining for me to go back and watch the middleschool/highschool level math to see how you explain them (I plan to be a math teacher), but these higher level videos are what help me.

[@davidnguyen7785]

you are a lifesaver, my uni course explains things so confusingly and this just made me understand immediately

[@HypnotizeCampPosse]

patrickJMT The way you did this video (going through all the tiny steps and showing the method of solving by emilination without and with a matrix, and graphing the first problem) was extremely helpful and helped me validate these as methods of solving these kind of problems. Thanks brah!

[@rickimarukurosaki1703]

That was bloody brilliant!!! I'm studying from home and you have really helped me understand this way better than any textbook ever could.

[@badge011193]

I have always used you in my calculus classes but didn't realize you also did vids for linear algebra! I wish I would have known this sooner! You are helping me pass my class and therefore become an engineer, so thank you. SO MUCH, you da man cool guy!

[@patrickjmt]

@ryantheleach thanks for letting me know! it sounds ok on my end, or i would have fixed it by now. a few glitchy noises, but nothing terrible i hope

[@unSOKOLATOULIS]

Patrick,you are by far the best math tutor I've ever encountered

[@jayzeus7]

I love these new Linear Algebra videos. They're being released just after we go over the subject so I can go back and get more review. You're the best Patrick!!!!~~~!!~~!

[@timugin]

Your Video is one of the best I have seen man ! Very good job. You are really good !

[@mdarifulislam7082]

this video cleared my confusion between trivial and nontrivial solution. Thanks for this amazing video. Peace

[@jackwhitehead4149]

I feel like everyone talks about how it'd be awesome to live in Binging With Babish's apartment and get food but no one talks about how awesome it would be to be PatrickJMT's roommate in college and get LITERALLY ALL THE HELP EVER.

[@SamiUllah-si8ck]

One word -> OUTSTANDING

[@jazzm5557]

Watching the first part of this video where you did the basic system of equations example from Algebra made me miss how simple math was back then 😂😭 it's been at least 8 years since I did math like that lmao

[@Bubbleegirl21]

Thanks for your help. I couldn't understand why the book was saying the answer was linearly dependent for my problem set. Once I watched your video I realized that the book hadn't explicitly said that linearly dependent systems have nontrivial solutions. Therefore I was getting nontrivial and trivial confused! Sometimes they write this stuff so confusing! I may watch more of your videos if I need help in studying for my final. Thanks. You have very nice handwriting btw.

[@abugslife2461]

Thank you!!! Online school sucks, but your videos are awesome!! :)

[@JonathanSampson-g2b]

Thanks for a great explanation!

[@habibafareed6295]

Thnxx for explaining in short time with such admirable quantity

[@adesinaadeyemo4647]

Kudos man, you give me some kinda easy ways of row reducing matrix system

[@iPranjalDas]

I'm in my final year of graduation and my concepts were cleared just now after watching this video lol

[@cparnin]

You should be America's math teacher for all courses. A video each step of the entire way...

[@patrickjmt]

@3croN i have the input as loud as it will go... do not know if they sell pre-amps to boost the signal.

[@tkmazurek]

Don't forget about Canada. I've heard at least 4 other people in my classes mention patrick.

[@VoidShadowMoon]

Really useful! Thanks for helping me understand a concept that my teacher cannot teach me!

[@imbsalstha]

well,u made it,u were only mine last hope .thanx 4 explaining it

[@niraj8668]

God bless this guy

[@patrickjmt]

maybe one day :)

[@patrickjmt]

@timugin glad you like 'em :)

[@patrickjmt]

@SuvinRK yep, if it is trivial, that is correct

[@sheePuuz]

Very well explained! Your videos are great!

[@ItsKeshini]

Hi Patrick, am still watching this video right now but just to mention, I searched on KZbin for videos explaining Trivial solution and Non Trivial solution and read lots of notes but in vain. I have to do self learning and I found your video helpful and I love how you explain taking your time but I have a question that is, how do you know which row to add or substract or multiply or divide by a number. Could you please help me with this I really need someone to explain this to me and KZbin classes are my only solutions. Thanks in advance From Mauritius.

[@Adkorane]

patrick, thank u man, i realy enjoy ur grt vedeos, keep on

[@Abujazzar]

If I was a poet I will praise you.Thanks a lot

[@MalaikaBasharat-vm4tf]

It's very informative sir 😊

[@patrickjmt]

excellent

[@toluwanimiadeyemo8099]

thanks for making it easy

[@carmeloanthony338]

you my new teacher

[@sajidshahnawaz8127]

KZbin should just give us a certificate for graduating from watching these amazing math videos, then I won't have to spend so much money on my bs university...

[@HonestAuntyElle]

@patrickJMT you could probably boost it in post-processing but the audio is fine.

[@RahulKumar-db9fd]

Well explained 👍

[@thies2us]

I enjoy your videos!!!

[@CalvinMaighan]

Ya, if only I could take the money i spent at school back to give it to the person actually teaching me something!

[@patrickjmt]

at least, my guess is that is what will have in your example

[@matthiasheinrichs2499]

Patrick, isn't it easier in the last example to just continue your row-reduction and bring the matrix back to it's reduced echelon form? this way you'll get | 1 0 0 0 | = X1 = 0 | 0 1 0 0 | = X2 = 0 | 0 0 1 0 | = X3 = 0 Would'nt that be the quickest way?

[@terminatortscc1]

patrickJMT SIR THANK YOU FOR SAVING THE WORLD FROM EVIL MATH TORTURE.

[@s.r.shourav2965]

Great job!!!

[@mmanagengcaroline3219]

thank you very much ♥♥

[@GRANDBALOCH]

good explanation

[@forlornreaper]

the playlist is backwards! but the content is fantastic! hope you fix it if you can.

[@fitimio001]

I like the part where he says the words. Its good stuff.

[@patrickjmt]

thanks :)

[@Abdullah-lh3zl]

Sir! Pl. tell me that when we'll get infinitely many solutions???

[@alycatherine]

i know how to get infininte solutions! i know im late... but the equations need to be the same. the variables and coefficients need to be the same. it may take a bit of simplifying though.

[@abdifatahshibrahim90]

Smile. Fantastic fan thanks lecturer

[@nilufargh]

well, Thanks a lot, it was a great video. But I just have a question, that is nontrivial solution only for homogenous system? cuz I'm pretty sure I've seen many examples that they weren't actually homogenous but they were forced to get parameter, therefore they had nontrivial solution. " The system has nontrivial solution with fewer variables than equation" Would be wrong , right?

[@hourtbora3072]

Are homogeneous systems of linear equations always consistent? Why? Is it true if a system of equation has more then one solution, then it must have an infinite number of solutions? Does a homogenous system always have an infinite number of solutions?

[@TheMrJoltz]

You make all these linear problems seem.... trivial....

[@patrickjmt]

@michaelpostal sounds just fine on my computer when i watch it

[@patrickjmt]

@PhxPride1 good timing!

[@pyroticmaniac]

This kind of stuff seems really intuitive and obvious, but I'm having a problem with a matrix that's 2x4. 4 variables with only 2 equations makes it pretty rough to solve, reduce, whatever. Any tips?

[@Chr0nalis]

Yes , I'm sure the While House cares deeply about the youths education...

[@seun2461]

+patrickJMT or anyone who knows, is this related to the wronskian, for my test I have to learn how to solve second order linear eqns using the Wronskian

[@johnstobbart]

Just America? He helps us hunters and gatherers in South Africa too, you know! And yes, it took me days of fighting through thick bush and hungry lions to get to a computer.

[@notpiccaboo142]

thank you from 2020

[@jhanepaulinesusi7521]

Hi, sir! How about solving 2 by 4 matrix using Gauss Jordan Reduction? Is that possible to use that tricks in that situation? God bless.

[@seun2461]

also how do you know to do -1R_1+ R_3 = R_3

[@HeyClare]

i'm sorry of this is not a great question to ask, but if the matrix has free variables (ie there's more variables than equations), can the system have a trivial solution?

[@apoorva158]

what about non trival?:-(

[@patrickjmt]

thanks! :))))

[@AnantoYusufW]

thanks.. is trivial solution only for homogeneous?

[@steven3474]

in my solution book,in some cases they use the same variable for two different free variables. for example x3=a and x4=a? why is this?

[@umerbashir2875]

u still alive patrick

[@artistiaay5512]

In the last example, Why didnt you convert the matrix into RREF before finding the solution!?

[@devampatel7710]

so if there are only trivial solutions, does that mean that the equations are linearly independent?

[@sorakmaz413]

thank you i love you

[@simondungeon1218]

nicely taught..

[@abdifatahshibrahim90]

when both variables are (0,0) the equation is said to be Trivial sol

[@ashtonhunter3761]

The only reason i make it through college is b/c of you. lol Thanks for the video.

[@ShawkyJames]

is this the general solution?

[@fhn888]

Thanks a lot!!!!!

[@muhammadaftab5798]

That's great where is part 2

[@minakshi...6623]

After 10 years

[@kennethlorenzg]

Hey man how do i identify free variables in the equations?

[@MrShacky96]

why doesn't the sound of any of your videos work anymore? am i the only one experiencing this?

[@patrickjmt]

Yes

[@kerrickmcneil7671]

+MrShacky96 try going into your control panel>hardware and sound>sound, then configure your speakers for stereo. may help.

[@JustKyzuuh]

+MrShacky96 Yeah make sure you don't have any surround sound turned on, it messes up the audio in his videos.

[@erickrobles6365]

+patrickJMT Hes alive! thanks for your vids btw. do you happen to have a video for wronskian problems and what its use is.

[@deepaksinghbungla5971]

This is for which Grade/Class ?

[@anirbandas521]

Thanks buddy

[@jiggskat]

yes..i am a teacher in mathematics..yet i didnt learn this in high school and in college so i am having a hard time encountering this in my master's degree..hehehe

[@patrickjmt]

you will have two free variables with infinitely many solutions - i have videos like this

[@dudewheresmycar3618]

Is the trivial solution always equal to 0?

[@karla011302]

why did you multiply 2(2x-2y)=o why the 2??

[@philipT8989]

i dont understand, why do u have to solve anyything? if the trivial solution is when everything is = 0 just but x1 and x2 ... xn = 0 and its always be zero?

[@desrick2006]

You lost me on the graphing part. Where did u get that -5 from?

[@jayashree9346]

super example

[@jayashree9346]

sir

[@smitasingh1492]

Ty ❤️

[@thebridgeofsanity]

wait so does that mean that a trivial solution is only one where all the solutions are zero?

[@racerdude212]

Is |A'| also equals to zero

[@3croN]

Please make your videos more louder, I dont know if its my headphones fault, but you are too quiet, please :)

[@3croN]

THis is amazing :D

[@Dan-bg5fm]

this is linear algebra??

[@michaelpostal]

Voice is too low. Keep up good work.