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Linear Algebra Example Problems Subspace Example 5
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http://adampanagos.org • Course website: https://www.adampanagos.org/ala • This subspace example problem is a little different from the previous examples. In this problem we work with P2, the set of all polynomials of at most degree 2. • We show that P2 is a subspace of Pn, the set of all polynomials of at most degree n for n greater than or equal to 3. • We do this by showing the following: • 1) P2 is a subset of Pn • 2) P2 contains the zero vector • 3) P2 is closed under vector addition • 4) P2 is closed under scalar multiplication • This problem is interesting since the objects we deal with are polynomials instead of vectors in R2, R3, etc. This emphasizes the fact that vectors spaces are very general concepts. A vector space is a collection of ANY objects that satisfy the properties of a vector space. Sometimes this really means vectors, other times the collection of objects can be polynomials, matrices, etc. • 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!
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