Skip to main content
\(\newcommand{\identity}{\mathrm{id}} \newcommand{\notdivide}{{\not{\mid}}} \newcommand{\notsubset}{\not\subset} \newcommand{\lcm}{\operatorname{lcm}} \newcommand{\gf}{\operatorname{GF}} \newcommand{\inn}{\operatorname{Inn}} \newcommand{\aut}{\operatorname{Aut}} \newcommand{\Hom}{\operatorname{Hom}} \newcommand{\cis}{\operatorname{cis}} \newcommand{\chr}{\operatorname{char}} \newcommand{\Null}{\operatorname{Null}} \newcommand{\lt}{<} \newcommand{\gt}{>} \newcommand{\amp}{&} \)

Section3.3Week 7 (Jul 9-13)

This week, we'll finish up the key idea of Chapter 3: how a basis can be used both to describe the (infinitely many) elements in a vector space using a much smaller set, and to define a system of coordinates on that space. We'll extend that knowledge to how bases determine subspaces -- that is, smaller vector spaces residing within bigger ones. Subspaces will play an important role in the concluding chapter of our course, and writing down a basis is among the best ways of understanding and communicating about subspaces.

We'll be taking the sections in Chapter 3 a little out of order, coming back for 3.4 Determinants when the final chapter begins.

To do this week:

By Friday 7/13:

  1. Submit Quiz 6R via Blackboard.

By Saturday 7/14:

  1. Read and annotate 3.2: Bases and Coordinate Systems
  2. Read and annotate 3.5: Subspaces of \(\mathbb{R}^p\)
  3. Watch here for Lectures 6 and 7.

Subsection3.3.1Using the Inverse of a Matrix

Subsection3.3.2Coordinate Vectors and Changes of Basis