Linear Algebra Example Problems - Subspace Example #2

We work with a subset of vectors from the vector space R3. We show that this subset of vectors is NOT a subspace of the vector space.

In general, given a subset of a vector space, one must show that all of the following are true:

1) Contains the zero vector, 2) Is closed under addition, and 3) Is closed under scalar multiplication.

If any of these fail, the subset is not a subspace. It turns out that for the particular example worked in this problem none of these properties are true.

[ThePowersofDerp]

Thank you so much for being able to explain something so simple that my Ph.D. Professor couldn't convey in 2 hours!!!

[jrp]

I found this example extremely helpful. Seeing the failures really helped fill in some blanks for me. Thanks for the help!

[dadadadogo]

I like these simple exercises, they help me understand the concept of subspaces. thank you!

[austinwilliams]

Wow, this video cleared up so many misconceptions I had. My final is tomorrow and this is the first time understanding what "closed under addition means."

[Qiq-ogms]

just want to say thank you so much for all these helpful videos!
ive been watching your videos for my linear algebra class, and they have been very helpful

[dianampm]

Amazing videos that I keep coming back to remember the basic ideas and the applications of all the theorems. Thank you, again! Hope you come to Portugal, you will love it (I´d recommend Lisbon or Porto!!)

[ouiji.]

Your 2's are suspiciously similar to Z. I was confused for a moment with what you were saying and what was being presented.

[helloes]

thank you a lot! it reaIIy helped me to understand the concept

[Chrisymcmb]

thanks, your tutorials came in clutchhhh

[Fnxpibv]

This helped alot!! thanks for taking the time to explain the other axioms!

[dipti]

Thank you ... adam it was very helpful video.. i did not understand anything my sir taught me....but u did... thanks a lot😊

[mariovelelafierro]

Thank you!! for the help I was finally able to understand vectors spaces and subspace

[defnotsolrac]

Awesome Video, really helped me out understand this concept!!!

[charlesamofordjuoh]

continue making linear algebra videos please!!!

[gincoopland]

Thank you so much! the text book just says closed under addition and scalar multiplication but it doesn't really show how we checked these!

[jandro]

This video was really helpful, thank you!

[EmapMe]

What if you wanted to check if the set of vectors was a subspace of R2 or R6? Would you just do the exact same thing?

[mariachiforhire]

Ooo that's a 2?? I thought it was a capital Z. Face palm on my part.

[Turtlesz]

thanks for this video!! Just one question, for scalar multiplication, would 2rc-sc and rc+sc meet the requirements? Why or why not?

[josenator]

how about if you get a form that looks like this : {(x, y) ∈ R
2
| x ≥ 2y}. How would you tackle a problem like this