Linear Algebra Example Problems - Subspace Example #1

http://adampanagos.org

Course website: https://www.adampanagos.org/ala

Join the YouTube channel for membership perks:
   / @adampanagos  

We work with a subset of vectors from the vector space R3. We show that this subset of vectors is a subspace of the vector space via a useful theorem that says the following:

Given a vector space V, the span of any set of vectors from V is a subspace of V.

Since we're able to write the given subset of vectors as the span of vectors from R3, the set of vectors in this problem is indeed a subspace of R3.

Another way to work this problem is to show that the set of vectors satisfies the following 3 properties: 1) Contains the zero vector, 2) Is closed under addition, and 3) Is closed under scalar multiplication.

Course website:
https://www.adampanagos.org/ala-appli...

If you enjoyed my videos please "Like", "Subscribe", and visit http://adampanagos.org to setup your member account to get access to downloadable slides, Matlab code, an exam archive with solutions, and exclusive members-only videos. Thanks for watching!