Linear Independence and Linear Dependence, Ex 1

Linear Independence and Linear Dependence, Ex 1. In this video, I explore the idea of what it means for a set of vectors to be linearly independent or dependent. I then work an example showing that a set of vectors is linearly dependent.

[holdenjones]

How to ace all first year math courses:
1- Go to class, try to learn the basics
2- Watch a Khan academy video to "gain some intuition" for subject
3- Watch every relevant Patrick JMT video to practice solving problems

4- Repeat throughout semester

[ryanmcguire]

You have been my prof for at least 3 classes in uni

[williamidakwo]

To save time if you're asked to determine whether or not the vectors are linearly dependent,
Take the determinant, if its = 0 it is linearly dependent if not it is linearly independent.

[adamfattal]

First time I watched your videos was in the 8th grade, when I was teaching myself calculus over the summer. I still find myself watching you in college when I need to review over a topic or get some practice. Thank you for all that you do, Patrick! You're changing peoples' lives, so cheers to that

[dapoog]

I love it when my professor just decides to never show up, and still took the test as if he had been there, I literally only have a table of contents and YouTube

[maraltsogt]

guess who is watching this after 12 years later. ME

[sandblaster]

Such a good tutorial, even 9 years later. Thanks!

[Turgutgncfb]

Thank you for the video, but I think it is a long way, if you would like to find the case either is it linearly dependence or independence, you can find determinants. If determinants doesn't equal to zero, it means INDEPENDENCE, but if equal then DEPENDENCE (linearly.)
BEST REGARDS FROM AZERBAIJAN

[youzhenzhang]

patrick jmt!!! you've helped me all throughout high school and college!! you rock my dude

[tamzidchowdhury]

I've commented this about 1000 times in your videos, but God Bless You!!

[ibrahimsayed]

Thank you Mr Patrick i remember about 10 years before when i was in 6th or 7th grade i have studied alot of exponential powers from your videos and now studying the concept of linear independence to pass my data science certificate i wholeheartedly respect you ... i am glad you still make videos for the students hope you are in good health :)

[higgsbp]

Simple explanations for simple concepts. My teachers somehow managed to make this convoluted. In 15 minutes you explained more than they did in 2+ hours. Kudos and much thanks:)

[fredrikpettersen]

Yes they do, but there is a difference between knowing the subject and being able to teach it. Patrick is a very skilled teacher, and has helped me a lot. :)

[stephendavis]

You're the best!!! I have passed soooo many classes solely because of your videos.

[Usagimusical]

This is the third year that I have been referencing these math videos, and I must say you're a fantastic instructor!
I definitely credit you for developing my passion for math!

cheers,
Janice :)

[muhammadzaid]

I started watching his vids in freshman year high school, now I am a freshman in college

[izzystreaks]

By the way Patrick is the reason why I have been getting through engineering school, If you guys really do love him that much I suggest donating to him! He has a website and tbh he deserves it!

[TheGheezoinky]

Thank you for this and everything else that you do. You just allowed me to ace my midterm. :)

GodBless! (if that's the kind of thing you believe in)

May the universe be kind to you.

[Dirkadirky]

Thanks for making these videos! I'm taking matrix algebra right now but I got a little behind. Your videos have helped me catch up! They're well made and you explain things well

[electrichorror]

Man... You deserve more credit you are the man!!!