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Section2.2Week 3 (Jun 4-8)

In Chapter 1 you built the most important computational skills you'll need in the first half of our course: row-reduction, identification of pivot positions, and expressing solutions of linear systems in parametric form. In Chapter 2, on top of these skills, we'll build the conceptual scaffold of linear algebra.

It all begins by introducing you to vectors, the real players on the stage of linear algebra, and matrices, the directors on the stage giving the players their plot. Both vectors and matrices start out as convenient tools, giving us the ability to think of several quantities or equations as a single object, but pay close attention this week to the underlying properties that make them the "right" tools. What makes a vector a vector, and what makes a matrix a matrix? Focusing on these properties will help you in the future to do one of the most important things our course can train you to do: spot the opportunity to use linear algebra when it arises in new contexts you've never seen before.

To do this week:

By Monday 6/4:

  1. Submit Quiz 2R on Blackboard.
  2. Submit Portfolio 1 on Blackboard.

By Tuesday 6/5:

  1. Review the Pecha-Kucha project assignment ( Section 2.5 ) and respond to the Flipgrid video prompt here: https://flipgrid.com/278e55.
  2. Read and annotate 2.1: Vectors and linear combinations https://via.hypothes.is/http://merganser.math.gvsu.edu/david/linear.algebra/ula/ula/sec-vectors-lin-combs.html
  3. Read and annotate 2.2: Matrix multiplication and linear combinations https://via.hypothes.is/http://merganser.math.gvsu.edu/david/linear.algebra/ula/ula/sec-matrices-lin-combs.html

By Wednesday 6/6:

  1. Watch for Lecture 3 here on Wednesday.
  2. Participate in Activity 2.2.2 via EdPuzzle: https://edpuzzle.com/assignments/5b14977fb6179c40a8a54e52/watch
  3. (Suggestion) Review the Proof Portfolio problems ( Section 4 ) for this chapter and start working on a couple of them in Overleaf.

By Thursday 6/7:

  1. Submit Quiz 3 via Blackboard.

By Friday 6/8:

  1. Participate in Activity 2.2.5 via EdPuzzle: https://edpuzzle.com/assignments/5b149f4bb6179c40a8a57ea4/watch
  2. (Suggestion) Review WeBWoRK's new set of available problem sets and complete as many problems as you can at this point in the material.

By Monday 6/11:

  1. Submit Quiz 3R via Blackboard.

Subsection2.2.1Linear combination "powers" linear algebra

You can play with the interactive tools shown in this video here: Section 1.

Subsection2.2.2Linear systems and linear combinations

You can play with the interactive tools shown in this video here: Section 1.

Subsection2.2.3The matrix-vector equation \(A\vec{x}=\vec{b}\)

You can play with the interactive tools shown in this video here: Section 1.