This section introduces the concept of a basis of a subspace. In effect, a basis can be through of as unit axis vectors of a coordinate system. This brings together the concepts of linear independence and spanning that we have already seen. So a big part of the section is devoted to using tools that we already have to produce a basis of a space. In this section the examples are very important for understanding.
You should reinforce your reading by doing some of the odd-numbered problems in the various parts of the Exercises. In addition to the numerical questions, think about #30 and #31 and apply what these problems say to #33 and #35.
(Show your work)