Applied Mathematics 1411A/B Chapter Notes - Chapter 4.5.2: Linear Combination, Linear Independence, Moveon.Org
30 Dec 2018
School
Department
Professor
Document Summary
The rest of this section is talking about the subtle interrelationships among the concepts of linear independence, spanning sets, basis and dimension. Let s be a nonempty set of vectors in a vector space v. a) b) If s is a linearly independent set, and if v is a vector in v that is outside of span(s), then the set. S u {v} that results by inserting v into s is still linearly independent. If you start with a set s of two or more vectors in which one of the vectors is a linear combination of the others then that vector can be removed from s without affecting the span(s). a. So that vector can be removed without affecting the other set that is defined as all the possible linear combinations of s. Let v be an n-dimensional vector space, and let s be a set in v with exactly n vectors.
