Week 3
Matrices

Business

The start of the week email. No need to reread it if you received it. It's just linked here in case anyone accidentally deleted it (it's happened before 🥺). Definitely let me know if you didn't receive it though so we can figure out why not.

Matrices

Matrices: Terminology and examples 📄 Slide Show
If we're going to work with matrices, we need a way to talk about them, and that requires a bit of terminology. Terms are defined here that I will use going forward.
The slide show also gives several examples of applications of matrices to give you an idea of the wide variety of things they are used to model.
A brief history of matrices ↗︎
A nice brief illustrated history of matrices. Read a comic to learn math! 😎
Example: Solving a 2x2 system of equations using matrices 📹 Pencast 7:31|📘 PDF
Side-by-side solution of the Pet Biscuits problem using algebraic notation and matrix notation.
Allowable matrix transformations 📹 Pencast 5:12|📘 PDF
The transformations you can perform on a matrix depend on what the matrix represents. Since our matrices represent systems of equations we can do anything to the rows of our matrices that you could do to equations:
  1. Multiply all the entries in a row by a number
  2. Add (or subtract) one row from another
  3. Generalizing 1 and 2: Add (or subtract) any multiple of one row from another.
  4. Interchange rows.
  5. Interchange columns (but not the rightmost one).
Gaussian elimination (Pivoting) 📹 Pencast 10:52|📘 PDF
In this pencast I explicitly identify the steps we go through to solve a system of equations using a matrix representation.
  1. Pivot around each element on the main diagonal of the matrix:
    1. Make the pivot element a 1,
      by dividing
      all the entries in the row by the pivot element.
    2. Make the other entries in the pivot column 0s,
      by adding/subtracting
      a suitable multiple of the pivot row from each other row.
  2. Read the solution from the final matrix.
Solving a 3x3 system using matrices: Example 1 📹 Pencast 15:30|📘 PDF
A step-by-step example of solving a 3x3 system of simultaneous equations using Gaussian elimination in a matrix.
Solving a 3x3 system using matrices: Example 2 📹 Pencast 12:02|📘 PDF
A second example of solving a 3x3 system of simultaneous equations using Gaussian elimination in a matrix.
Summary: Solving systems of linear equations using Gaussian elimination in matrices 📘 PDF
The title is quite the mouthful, but this is my capsule summary of the steps.
Teaching Excel how to solve 3x3 systems of equations for us 📹 Screencast 17:34
Pivoting is fun and all, but it is a mechanical process, which means it could be automated, and done by a computer. Let's do that.

Exercise Sets

Exercise Set 3 Part 1: Problems and Solutions Problems and Solutions
Due by 4 pm Monday January 25.

Assignment

Assignment 2 Due by 4 pm Friday January 29.

Try to submit PDF files of work done by hand or in a word processor.
Excel spreadsheet files should be sent as file attachments.
Google sheets can be submitted by sharing a link to them.