Math 251: Matrix Algebra for Engineers

Updates/Revisions to the Math 251 Course Webpages

• None as of yet

Links to other Math 251 Sites

• You can find more resources on the Math 251 websites for the following Camosun instructors:
  • Gilles Cazelais, especially his Course Notes and Resources page.
  • Leah Howard, including a complete set of course notes and also lecture videos
  • George Ballinger, who has sample tests and useful documents and links
  • Susie Wieler
• (You'll find some redundancy because we do share resources.)

Study Plan

Week 1: Sept 8 to Sept 11

• Section 1.1: The Geometry and Algebra of Vectors
  • My Lecture Notes: Part 1, Part 2 – these are skeleton notes from last year's lecture class. For more detailed notes, please check out Gilles Cazelais' Math 251 Course Notes Page.
  • Handout: Section 1.1: Properties of Vectors
  • We are omitting Binary Vectors and Modular Arithmetic from Section 1.1.
  • Leah's Videos: 1.1 Intro to Vectors (2 mins) and 1.1 Intro to Linear Combinations (4 mins)
• Section 1.2: Length and Angle: The Dot Product
  • My Lecture Notes: Part 1, Part 2, Part 3, Part 4 (can leave Parts 3 and 4 until next week and still be on track)
  • Leah's Videos: 1.2 A Proof about The Dot Product (5 mins) and 1.2 Scaling Vectors (4 mins)
  • Conceptual Videos: Zach Star's video on applications of the dot product: watch the first 2:30 min
• WeBWorK Assign0, which is due the following week

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Week 2: Sept 14 to Sept 18

• Finish up Section 1.2
• Exploration: The Cross Product
  • My Lecture Notes: Part 1, Part 2, Part 3
  • Leah's Videos: Cross Product: Equation of a Plane Through Three Points (6 mins), Cross Product: Area of a Triangle in 3-d (4 mins), Determinants: Area of a Parallelogram in 2-d (3 mins), Determinants: Volume of a Parallelepiped in 3-d (9 mins)
• Start looking at Section 1.3: Lines and Planes
  • My Lecture Notes: Part 1, Part 2, Part 3, Part 4, Part 5 (can leave Parts 3 to 5 until next week and still be on track)
  • Handout: Section 1.3: Lines and Planes
  • Leah's Videos: 1.3 General and Normal Form (3 mins), 1.3 Vector and Parametric Form (6 mins), 1.3 Distance Between a Point and a Line (9 mins)
• WeBWorK Assign1, which is due the following week

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Week 3: Sept 21 to Sept 25

• Finish up Section 1.3
• Section 2.1: Introduction to Systems of Linear Equations
  • My Lecture Notes: Part 1, Part 2
  • Leah does not have videos for this section.
• Start working on Section 2.2: Direct Methods for Solving Linear Systems
  • My Lecture Notes: Part 1, Part 2, Part 3, Part 4
  • Handout: Section 2.2: Homogeneous Systems
  • Leah's Videos: 2.2 Gaussian Elimination (12 mins), 2.2 Gauss-Jordan Elimination (13 mins)
  • Conceptual Videos: watch the first 2:23 minutes of Zach Star's video on matrix manipulation to see what's actually going on when you solve a system
• WeBWorK Assign2, which is due the following week
• Fun link of the week: Mad Engineers

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Week 4: Sept 28 to Oct 2

• Finish up Section 2.2

• Test 1 covers the material up to this point. Here is a brief review of the topics covered.

• Section 2.3: Spanning Sets and Linear Independence
  • My Lecture Notes: Part 1, Part 2, Part 3, Part 4
  • Leah's Videos: 2.3 Span (7 mins) , 2.3 Linear Independence (11 mins)
• Section 2.4: Applications
  • Revised lecture notes coming soon!
  • Leah does not have videos for this section.

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Week 5: Oct 5 to Oct 9

• Section 3.1: Matrix Operations
  • My Lecture Notes: Part 1, Part 2
  • Leah's Videos: 3.1 Matrix Operations (9 mins), 3.1 Powers of a Matrix (10 mins)
  • Conceptual Videos: Zach Star's video on applications of matrices: from 1:15 to 4:36 to see why we can use the inverse of matrix A to solve Ax=b

• Test 1 is tentatively scheduled for Wednesday of this week.

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Week 6: Oct 12 to Oct 16

• Section 3.2: Matrix Algebra
  • My Lecture Notes: Part 1, Part 2, Part 3
  • Handout: Chapter 3: Matrix Properties
  • Leah's Videos: 3.2 Span of a Set of Matrices (12 mins), 3.2 A Proof about the Transpose (3 mins)
• Section 3.3: The Inverse of a Matrix
  • My Lecture Notes: Part 1, Part 2, Part 3, Part 4
  • Leah's Videos: 3.3 The Inverse of a Matrix (8 mins), 3.3 Elementary Matrices (10 mins)

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Week 7: Oct 19 to Oct 23

• Section 3.4: The LU Factorization
  • My Lecture Notes: Part 1, Part 2
  • Leah's Videos: 3.4 LU Factorization (8 mins), 3.4 Solving using LU (6 mins)
• Section 3.5: Subspaces, Basis, Dimensions, and Rank
  • My Lecture Notes: Part 1, Part 2, Part 3, Part 4, Part 5,
  • Handout: Section 3.5: Change of Basis
  • Leah's Videos: 3.5 Subspaces (9 mins), 3.5 Rowspace, Columnspace and Nullspace (8 mins)
  • Conceptual Videos: Zach Star's video on matrix manipulation explains the null space, row space, and column starting at 2:25 and ending at 9:00

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Week 8: Oct 26 to Oct 30

• Section 3.6: Introductions to Linear Transformations
  • My Lecture Notes: Part 1, Part 2, Part 3
  • Leah's Videos: 3.6 Standard Matrix of a Linear Transformation (8 mins), 3.6 Image Under a Linear Transformation (7 mins)

• Test 2 covers the material up to this point. Here is a brief review of the topics covered: Part 1, Part 2.

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Week 9: Nov 2 to Nov 6

• Appendix C: Complex Numbers (Appendix C)
  • My Lecture Notes: Part 1, Part 2, Part 3
  • Leah's Videos: Appendix C: The Algebra of Complex Numbers (3 mins)

• Test 2 is tentatively scheduled for Wednesday of this week.

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Week 10: Nov 9 to Nov 13

• Section 4.1: Introduction to Eigenvalues and Eigenvectors
  • My Lecture Notes: Part 1, Part 2
  • Leah's Videos: 4.1 Eigenvalues and Eigenvectors (9 mins), 4.1 The Geometry of Eigenvectors (7 mins)
  • Conceptual Videos: Zach Star's video on eigenvectors and eigenvalues: watch the first 2:56 min for a nice conceptualization, including complex eigenvectors
• Section 4.2: Determinants
  • My Lecture Notes: Part 1, Part 2, Part 3
  • Leah's Videos: 4.2 Cramer's Rule (7 mins), 4.2 The Adjoint Formula for an Inverse Matrix (7 mins)

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Week 11: Nov 16 to 20

• Section 4.3: Eigenvalues and Eigenvectors of n × n matrices
  • My Lecture Notes: Part 1, Part 2, Part 3 – Josh M. was my substitute lecturer for Part 2
  • Leah's Videos: 4.3 Geometric Multiplicity (6 mins) , 4.3 Algebraic Multiplicity (13 mins) , 4.3 A Proof about Eigenvectors (5 mins) , Appendix C: Complex Eigenvalues and Eigenvectors (12 mins)
  • Conceptual Videos: 3Blue1Brown's video on eigenvectors and eigenvalues
• Section 4.4: Similarity and Diagonalization
  • My Lecture Notes: Part 1, Part 2, Part 3 – these are notes from 2017 since I had a substitute during this section in 2018
  • Leah's Videos: 4.4 Diagonalization (7 mins), 4.4 Powers of a Matrix and Diagonalization (8 mins)
• Start working on Section 5.1: Orthogonality in Rⁿ
  • My Lecture Notes: Part 1, Part 2, Part 3
  • Leah's Videos: 5.1 Calculations with an Orthogonal Basis (3 mins), 5.1 Orthogonal Matrices (4 mins)

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Week 12: Nov 23 to Nov 27

• Finish up Section 5.1
• Section 5.2: Orthogonal Complements and Orthogonal Projections
  • My Lecture Notes: Part 1, Part 2
  • Leah's Videos: 5.2 Orthogonal Complements (7 mins), 5.2 Orthogonal Decompositions (8 mins)
• Section 5.3: The Gram-Schmidt Process and the QR Factorization
  • My Lecture Notes: Part 1, Part 2
  • Leah's Videos: 5.3 The Gram-Schmidt Process (7 mins) , 5.3 QR Factorization (9 mins)

• Test 3 covers the material up to this point. Here is a brief review of the topics covered: Part 1, Part 2.

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Week 13: Nov 30 to Dec 4

• Section 5.4: Orthogonal Diagonalization of Symmetric Matrices
  • My Lecture Notes: Part 1, Part 2
  • Leah's Videos: 5.4 Orthogonal Diagonalization (11 mins), 5.4 The Spectral Decomposition (6 mins)

• Test 3 is tentatively scheduled for Wednesday of this week

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Week 14: Dec 7 to Dec 11

• Section 7.3: Least Squares Approximation
  • My Lecture Notes: Part 1, Part 2, Part 3
  • Leah's Videos: 7.3 Least Squares Approximation (8 mins)

• Review for Final Exam
  • My Review: Part 1, Part 2, Part 3