Homework for Span

1. When is a vector an element of a span?

Given a finite subset $S$ of a vector space $V,$ and a single vector ${\bf v} \in V,$ know how to determine when ${\bf v} \in \textrm{Span}(S).$
Note: Showing that ${\bf v} \in \textrm{Span}(S)$ will require actually expressing ${\bf v}$ as a particular linear combination of the vectors in $S.$

Homework:
- From http://linear.pugetsound.edu/html/section-S.html, do Exercises S.C15, S.C16, S.C17, S.C20, and S.C21.
  Note: Beezer uses the notation $\langle S \rangle$ for $\textrm{Span}(S).$ We will use the latter.
  Note: For Exercises S.C16, S.C17, and S.C21, express the vector ${\bf v}$ as a linear combination of vectors from the set $S.$