MATH 3200: APPLIED LINEAR ALGEBRA
Fall Semester 2021

5

Notes for the Chapters:

  1. Outline of Chapter 1
  2. Outline of Chapter 2
  3. Outline of Chapter 3
  4. Outline of Chapter 4
  5. Outline of Chapter 5

Lectures:

  1. Lecture 1: Matrices
  2. Lecture 2: More Examples of Matrices: Vectors
  3. Lecture 3: More Examples of Matrices: Adjacency Matrices of Graphs
  4. Lecture 4: Some Matrix Operations: Addition, Subtraction, Transpose, and Multiplication by a Scalar
  5. Lecture 5: Products of Matrices
  6. Lecture 6: Submatrices
  7. Lecture 7: Some Special Matrices
  8. Lecture 11: Introduction to Systems of linear Equations
  9. Lecture 12: Matrix Representations of Systems of Linear Equations
  10. Lecture 13: Matrices in (Row) Echelon Form and More on Back-Substitution
  11. Lecture 14: Solving Systems of Linear Equations by Gaussian Elimination, Part I
  12. Lecture 15: Solving Systems of Linear Equations by Gaussian Elimination, Part II
  13. Lecture 16: Introduction to Inverse Matrices
  14. Lecture 17: Using the Inverse Matrix to Solve Linear Systems
  15. Lecture 18: Finding Inverse Matrices by Gauss-Jordan Elimination
  16. Lecture 19: Properties of the Inverse of a Matrix
  17. Lecture 21: Introduction to Linear Combinations
  18. Lecture 22: Finding Linear Combinations and the Linear Span of a Set of Vectors
  19. Lecture 23: Vector Spaces
  20. Lecture 24: More on Linear Dependence and Linear Independence
  21. Lecture 25A: Definitions of Bases
  22. Lecture 25B: Applications of Bases; Parametrization and Change of Bases
  23. Lecture 26: The Rank of a Matrix
  24. Lecture 27: The Rank and Consistency of Systems of Linear Equations
  25. Lecture 28: The Null Space of a Matrix
  26. Lecture 29: The Rank and Theory of Solutions. How to Represent Solution Sets
  27. Lecture 30: Introduction to Linear Transformations
  28. Lecture 31: Introduction to Determinants: Definition, Examples, and Basic Properties
  29. Lecture 32: Calculating Determinants by Pivotal Condensation
  30. Lecture 33: More Properties of Determinants
  31. Lecture 34: Applications of Determinants to the Geometry of Linear Transformations
  32. Lecture 35: Calculating Determinants by Cofactor Expansion
  33. Lecture 36: Eigenvectors and Eigenvalues: Introduction
  34. Lecture 37A: Finding Eigenvalues
  35. Lecture 37B: Finding Eigenvectors
  36. Lecture 38: Eigenvectors and Eigenvalues of Inverse Matrices and Matrix Transposes
  37. Lecture 41: Norms and Distances
  38. Lecture 42: Inner Products and Orthogonality
  39. Lecture 43: Orthogonal Projections, Orthogonal Complements, and Orthonormal Bases

Conversations:

  1. Conversation 1: Hi!
  2. Conversation 2: Our first encounter with proofs
  3. Conversation 3: Adjacency Matrices of Digraphs
  4. Conversation 4: Our second proof
  5. Conversation 5: More about proofs. Translating assumptions of theorems
  6. Conversation 6: More about proofs. Translating conclusions of theorems
  7. Conversation 7: Introduction to Probabilities
  8. Conversation 8: Introduction to Markov Chains. weather.com light
  9. Conversation 9: More on Markov Chains. Making forecasts with weather.com light
  10. Conversation 10: More Applications of Markov Chains: Where is Waldo?
  11. Conversation 11A: Translating word problems into linear systems. Part I
  12. Conversation 11B: Translating word problems into linear systems. Part II
  13. Conversation 12: Solving systems of linear equations with back-substitution
  14. Conversation 13: Solving systems of linear equations
  15. Conversation 21: Marvin and Marilyn Go on a Diet
  16. Conversation 22: Applications of Linear Combinations to Foraging Bees
  17. Conversation 23: Applications of Linear Combinations and of the Linear Span to Systems of Chemical Reactions
  18. Conversation 24: Properties of the Linear Span
  19. Conversation 25A: Introduction to Linear Dependence and Linear Independence. Part I
  20. Conversation 25B: Introduction to Linear Dependence and Linear Independence. Part II
  21. Conversation 25C: Geometric Interpretation of Linear Independence
  22. Conversation 26: Bases and Dimension
  23. Conversation 27: An Application of Base Changes
  24. Conversation 28: The Rank of a Stoichiometric Matrix
  25. Conversation 29: The Rank and Theory of Solutions
  26. Conversation 30A: Matrix Representations of Linear transformations
  27. Conversation 30B: Linear transformations etc.: How are all these concepts related?
  28. Conversation 31: Where do these Names Eigenvectors and Eigenvalues come from?
  29. Conversation 32: Complex Eigenvalues
  30. Conversation 33: Full Sets of Eigenvectors. Part A
  31. Conversation 34: Eigenvectors and Eigenvalues of Matrix Transposes and Inverse Matrices
  32. Conversation 36: Applications of Eigenvectors to Markov Chains
  33. Conversation 37: Diagonalization
  34. Conversation 41: Least-Squares Solutions
  35. Last Conversation: The Final is Coming Up

Modules for self-study, practice, and review:

  1. Module 1: Examples of Matrices (Practice)
  2. Module 2: Summation Notation (Self-Study and Practice)
  3. Module 3: Vectors (Practice)
  4. Module 4: Adjacency Matrices and Degree Sequences of Undirected Graphs (Self-Study and Practice)
  5. Module 5: Addition, Subtraction, Transpose of Matrices and Multiplication by Scalars (Practice)
  6. Module 6: Adjacency Matrices and Degree Sequences of Directed Graphs (Self-Study and Practice)
  7. Module 7: Matrix Products (Practice)
  8. Module 8: Entering Matrices in MatLab and Properties of Matrix Multiplication (Self-Study and Practice; Uses MatLab)
  9. Module 9: Submatrices and Powers of Square Matrices (Self-Study and Practice; Uses MatLab)
  10. Module 10: Some Special Matrices (Practice)
  11. Module 11: What are probabilities, anyway? A very brief introduction to probabilities and probability distributions (Self-Study and Practice)
  12. Module 12: Estimating transition probabilities (Self-Study and Practice)
  13. Module 13: More on Markov Chains. Constructing Forecasts with weather.com light (Self-Study and Practice)
  14. Module 14: More Applications of Markov Chains. Where is Waldo? (Practice)
  15. Module 15: More Applications of Markov Chains. Waldo's Surfing Pattern. (Practice
  16. Module 21: Introduction to Linear Systems (Practice)
  17. Module 22: Matrix Representations of Linear Systems (Practice)
  18. Module 23: Translating Word Problems into Systems of Linear Equations (Practice)
  19. Module 24: Tools for Solving Linear Systems: Matrices in Row Echelon Form and Back-Substitution (Practice)
  20. Module 25: Elementary Row Operations and Elementary Matrices (Self-Study and Practice; Uses MatLab)
  21. Module 26: Gaussian Elimination, Part I (Practice)
  22. Module 27: Gaussian Elimination, Part II (Practice)
  23. Module 28: Introduction to Inverse Matrices (Self-Study and Practice)
  24. Module 29: Using the Inverses of Coefficient Matrices to Solve Linear Systems (Practice)
  25. Module 30: Gauss-Jordan Elimination (Practice)
  26. Module 31: Properties of Inverse Matrices (Self-Study and Practice)
  27. Module 41: Introduction to Linear Combinations (Practice)
  28. Module 42: Finding Coefficients of Linear Combinations (Practice)
  29. Module 43: Properties of the Linear Span of a Set of Vectors (Self-Study and Practice)
  30. Module 44: Applications of Linear Combinations and of the Linear Span to Movement in Three Dimensions (Practice)
  31. Module 45A: Applications of Linear Combinations and of the Linear Span to Systems of Chemical Reactions: Reaction Vectors (Self-Study and Practice)
  32. Module 45B: Applications of Linear Combinations and of the Linear Span to Systems of Chemical Reactions: The Stoichiometric Matrix (Self-Study and Practice)
  33. Module 46: Vector Spaces and their Spanning Sets (Self-Study and Practice)
  34. Module 47A: Definitions of Linear Dependence and Linear Independence (Practice)
  35. Module 47B: More on Linear Dependence and Linear Independence (Practice)
  36. Module 48: Bases of Vector Spaces (Practice)
  37. Module 49: The Rank of a Matrix (Practice)
  38. Module 50: Consistency and the Rank (Practice)
  39. Module 51: Applications of the Rank to Systems of Chemical Reactions (Self-Study and Practice)
  40. Module 52: The Null Space of a Matrix (Practice)
  41. Module 53: The Rank and Theory of Solutions, Part I: Three Theorems (Self-Study and Practice)
  42. Module 54: The Rank and Theory of Solutions, Part II: How to Represent Solution Sets (Practice)
  43. Module 55A: Linear Transformations (Practice)
  44. Module 55B: Matrix Representation of Linear Transformations (Self-Study and Practice)
  45. Module 61: Introduction to Determinants (Practice)
  46. Module 62: Computing Determinants by Pivotal Condensation (Practice)
  47. Module 63A: More Properties of Determinants (Practice)
  48. Module 63B: Proofs of Some Properties of Determinants (Practice)
  49. Module 64: Determinants and Properties of Linear Transformations (Practice)
  50. Module 65: Calculating Determinants by Cofactor Expansion (Practice)
  51. Module 66: Introduction to Eigenvectors and Eigenvalues (Self-Study and Practice)
  52. Module 67A: Finding Eigenvalues (Self-Study and Practice)
  53. Module 67B: Finding Eigenvectors (Practice)
  54. Module 68A: Eigenvectors and Eigenvalues of Inverse Matrices and of Matrix Transposes (Practice)
  55. Module 68B: Finding Eigenvectors and Eigenvalues in MatLab (Self-Study and Practice)
  56. Module 71: Applications of Left Eigenvectors to Markov Chains (Self-Study and Practice)
  57. Module 72: Diagonalization (Self-Study and Practice)
  58. Module 81: Norms and Distances (Self-Study and Practice)
  59. Module 82A: Inner Products and Orthogonality (Practice)
  60. Module 82B: Properties of Inner Products (Self-Study and Practice)
  61. Module 83: Projections, Orthogonal Complements, and Orthonormal Bases (Practice)

Review:

  1. Module 101: Suggested Review Problems for the Final (Review)

© 2021 Winfried Just
Last modified December 5, 2021.