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

Section2.3Week 4 (Jun 11-15)

Hopefully, your understanding of what linear algebra is "about" evolved last week. Linear algebra is, at its heart, the study of vectors and their properties -- as well as the ways in which matrices, acting by multiplying, transform vectors from domain to range. The algebraic properties of vectors and matrices you dwelled on last week will be your constant companions throughout the entire rest of the linear algebra story.

This week, we'll develop the tools to ask and answer one of the most fundamental questions in all linear algebra: is a collection of vectors linearly independent? In other words, does each of the vectors in the set "tell its own story?" Or would the story remain the same if one or more of the vectors were removed from the set? This seemingly basic idea will reverberate through the rest of our course, so be sure you take the time this week to process it, from the mechanics (how do I tell whether a given set of vectors is independent?) to the concepts (why is it important to know whether a set of vectors is independent? What does this question have to do with matrices and linear systems?)

This is also the week to draft your Pecha-Kucha script. (Click here for assignment details.) The goal of your Pecha-Kucha is to introduce the viewer to one key definition or concept from linear algebra, and this week's topics are prime for such an introduction. So draft what you want to say in your presentation and remember, the word count should be such that you can comfortably speak it in the Pecha-Kucha's 6-minute-40-second time frame!

To do this week:

By Monday 6/11:

  1. Submit Quiz 3R via Blackboard.

By Tuesday 6/12:

  1. Read and annotate 2.4: The span of a set of vectors https://via.hypothes.is/http://merganser.math.gvsu.edu/david/linear.algebra/ula/ula/sec-span.html
  2. Read and annotate 2.4: Linear independence https://via.hypothes.is/http://merganser.math.gvsu.edu/david/linear.algebra/ula/ula/sec-linear-dep.html

By Wednesday 6/13:

  1. Participate in Activity 2.3.3 part 1 via EdPuzzle: https://edpuzzle.com/assignments/5b202db81c6c2340af2e1296/watch
  2. Participate in Activity 2.3.3 part 2 via EdPuzzle: https://edpuzzle.com/assignments/5b2042a71c6c2340af2e3e6a/watch

By Thursday 6/14:

  1. Upload a video explaining an application of linear independence to our class Flipgrid: https://flipgrid.com/aa9d1c.

By Friday 6/15:

  1. Watch for Lecture 4 below.
  2. Submit Quiz 4 via Blackboard.
  3. Submit your Project 1 script draft via Blackboard.
  4. Participate in Activity 2.4.3 via EdPuzzle: https://edpuzzle.com/assignments/5b2101788b267f407197abf5/watch

Subsection2.3.1Span and Linear Independence

Subsection2.3.2The Invertible Matrix Theorem