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

Homogeneous Systems of Linear Equations - Trivial and Nontrivial Solutions, Part 1. In this video, I show what a homogeneous system of linear equations is, and show what it means to have only trivial solutions. In the next video, I work out an example that has nontrivial solutions.

#maths #algebra #linearalgebra #homogenous #homogeneous #homogeneousequations #trivial #linearsystems

[erikolson]

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.

[arwaa]

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

[MiguelGonzalez-kphq]

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

[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!

[davidnguyen]

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

[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.

[unSOKOLATOULIS]

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

[jazzm]

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

[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

[rickimarukurosaki]

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

[badge]

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!

[ItsKeshini]

Hi Patrick, am still watching this video right now but just to mention, I searched on YouTube 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 Youtube classes are my only solutions.
Thanks in advance
From Mauritius.

[patrickjmt]

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

[Bubbleegirl]

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.

[abugslife]

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

[jackwhitehead]

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.

[mdarifulislam]

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

[jayzeus]

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!!!!~~~!!~~!

[cparnin]

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

[timugin]

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