Linear Algebra

Office Hours

Room 443, in the DMF Center for Science and Mathematics (near the Rondileau Campus Center).

• Monday 2:00-3:00 and Tuesday/Thursday 3:45-4:45

You can also drop in and ask me a question:

• Any time you find me in my office (DMF 443).

Syllabus

• The Syllabus for Math 202. This is your source for course pacing, grading, and some helpful hints on group work and studying.
  
  
• You can access the online homework system via a link on the course page at http://blackboard.bridgew.edu.
  
  

1.1 - Solving Systems of Equations

• Video: Learning to solve systems of linear equations
  
• PDF: several scanned examples
  
  
• Video: Reduced Echelon Form, and the General Strategy for Solving Matrix Systems
  
  
  
• Handout: Pivots, Reduced Echelon Form, and a Strategy for Row Reduction
  
  
• The Augmented Matrices Practice Quiz and Solutions
  
  
• Solving systems of equations by hand means creatively trying to decide what step will be the "simplest". If you decide to always use the same kind of tricks, you can write down an algoritm, or precise strategy. The pages below generate random matrices, and then solve them using the relevant algorithm. Try refreshing the page to see how the same strategy solves systems with different properties.
  
  Classical Gaussian Elimination
  with smaller matrices
  with larger matrices
  
  Euclidean Algorithm Elimination
  with smaller matrices
  with larger matrices
  
  LCM Strategy
  with smaller matrices
  with larger matrices
  
  Using all three strategies
  a single matrix solved using all three strategies (scroll down to see the other strategies)

1.2 - Reasoning about Systems of Equations

• Handout: Theorem 2 and Matrix Notation
  
  
• Video: Synthesis (finding h to make a system consistent, example 1 of 2)
  
• Video: Synthesis (finding h to make a system consistent, example 2 of 2)
  
  
  
• Reasoning Logically with If and Then. This Handout summarizes the basic moves you can (and cannot) make when you have an "If/Then" statement.

1.3 - Vectors and Vector Equations

• Slides: Two Vectors Generate a Lattice (Graph Paper). Click on the Right Arrow on the keyboard to advance the slides.
• Handout: Understanding Span\(\{\vec{v}_1,\vec{v}_2\}\) by looking at the Lattice Graph Paper They Generate.

1.4 - Matrices and the Matrix Equation

• Worksheet: Four Representations and Solutions
  
  
• Quiz II Review Worksheet: Spans (noun) and Spanning (verb) and Solutions

1.5 - Solution Vectors, and Counting the Number of Solutions

• Handout: the Possible Number of Solutions to a Matrix Equation and Answers

1.7 - Linear Independence

• Video 1: Introducing Independence
  
• Video 2: Understanding and Applying Independence
  
• PDF: Slides for Videos 1 and 2

Building a Bridge to Engineering

• To build bridges that are both safe, and also cost effective, you must be able to model the forces on the bridge members under various loads. Here are two videos made using Bridge Constructor Playground: Video 1 and Video 2
  
• Assignment - Building a Bridge
• Notes - Building a Bridge
• A Video Explanation Of Rope Bridges
• Wigner - The Unreasonable Effectiveness of Mathematics in the Natural Sciences
• Physics Background
  • A Brief Introdution to Force Components

Exam I Review

• Practice Problems for Exam I Review and Solutions

1.8 & 1.9 - Matrix Functions and Linear Functions

• Worksheet - Matrix Transformation and Solutions
• Geometric Transformations of R² and Solutions

2.1 - Matrix Operations

• Scaling, Adding, and Multiplying Matrices
  

2.3 - Characterizing Invertible Matrices

• Diagram - The Invertible Matrix Theorem Tree
• Worksheet - Proofs and Invertible Matrices and Solutions

Exam II Review

• Practice Problems for Exam II Review and Solutions

4.1 - Vector Spaces and Subspaces

• Common Core Standards and Principles

4.2 - Spaces Defined by Transformations

• Worksheet - Vector Spaces, Subspaces, and Special Spaces and Solutions
• Worksheet - Comparing Null(A) and Col(A) and Solutions

4.4 - Coordinate Systems

• Handout: Lattice Graph Paper and Coordinate Spaces

4.5 - Dimension of a Vector Space

• Handout - An attempt to draw R4

Final Exam Review

• Reveiw the material from Exam I
• Review the material from Exam II.
• Review Worksheet of Material Since Exam II and Solutions

Textbook Information

You will need both the textbook, and a lot of paper for notes, homework, and scrap paper.

Textbook: Linear Algebra and its Applications by Lay, Lay, and McDonald.
You can buy any edition of the book. The newest edition is available in the bookstore. You can order old editions online at Amazon: 4th Edition, 5th Edition, etc.

Again, I will not need the online access code, and I will not assign problems based on the numbers at the end of the book, so you may buy a (slightly) earlier edition. But I will expect that you are reading along in the book, and using it for extra practice.