Linear Algebra I

13-Week Lesson Plan

I teach this course over a 13-week semester, including a midterm covering the first six weeks of material. Each class lasts 1.5 hours (minus 5-10 minutes for taking attendance and perhaps other administrative stuff).

The chapters are entitled:

  1. Linear Equations in Linear Algebra
  2. Matrix Algebra
  3. Determinants
  4. Vector Spaces
Here is an approximate week-by-week progress report:
  1. (1.1) Systems of Linear Equations;
    (1.2) Row Reduction and Echelon Forms
  2. (1.3) Vector Equations;
    (1.4) The Matrix Equation Ax = b
  3. (1.5) Solution Sets of Linear Systems;
    (1.6) Applications of Linear Systems
  4. (1.7) Linear Independence;
    (1.8) Introduction to Linear Transformations
  5. (1.9) The Matrix of a Linear Transformation;
    (1.9B) The Matrix of a Linear Transformation (cont.);
    (1.10) Linear Models in Business, Science, and Engineering
  6. (2.1) Matrix Operations;
    (2.2) The Inverse of a Matrix
  7. (2.3) Characterizations of Invertible Matrices;
    (2.5) Matrix Factorizations
  8. --> midterm
  9. (2.6) The Leontief Input=Output Model
  10. (3.1) Introduction to Determinants;
    (3.2) Properties of Determinants
  11. (3.3) Cramer's Rule, Volume, and Linear Transformations;
    (4.1) Vector Spaces and Subspaces
  12. (4.2) Null Spaces, Column Spaces, and Linear Transformations
  13. (4.3) Linearly Independent Sets; Bases;
    (4.4) Coordinate Systems