MATH 251 - Matrix Algebra for Engineers
Announcements
None at this time.
Lecture Notes
In case they prove helpful, on D2L (online.camosun.ca) I have posted copies of lecture notes and voice-over video lessons that I created to support online learning during the early days of COVID-19. The materials are still fairly current, having changed little since then.
Homework Problems
Section Exercises: A list of recommended practice problems is available here. The exercises themselves are available here in a password-protected PDF file (3.2MB). The password will be provided in class.
Chapter Review Exercises: For extra practice, a list of recommended chapter review problems is available here. These exercises can be found in a PDF file, having the same password, which is available here.
Exercise Answers: Answers to most^{†} odd-numbered textbook exercises can be found at the back of the textbook or in the Student Solutions Manual, which contains more detailed solutions. Answers have not been included in the PDF files above because doing so would have exceeded the amount allowable for "fair use" under copyright rules. Two copies each of the textbook and solutions manual can be found on reserve at the Lansdowne library (in addition to copies at Interurban). You can view the reservation status of these books on the library's website.
^{†}The following exercise answers are not in the textbook, but are given below.
- Answers to Appendix Exercises
- Answers to Recommended Problems from Section Exploration: The Cross Product
- Answers to Recommended Problems from Section Exploration: Geometric Applications of Determinants
Assignments are due by the end of class on the due dates.
Assignment | Sections of Textbook | Due Date | |
Assignment 1 | Solutions | 1.1, 1.2, 1.3, Expl. Cross Product | TBA |
Assignment 2 | Solutions | 2.1, 2.2, 2.3, 2.4 | TBA |
Assignment 3 | Solutions | 3.1, 3.2, 3.3 | TBA |
Assignment 4 | Solutions | 3.4, 3.5, 3.6 | TBA |
Assignment 5 | Solutions | App. C, 4.1, 4.2, Expl. Determinants | TBA |
Assignment 6 | Solutions | 4.3, 4.4, 5.1, 5.2 | TBA |
Assignment 7 | Solutions | 5.3, 5.4, 7.3 | TBA |
Term Tests
Test | Sections of Textbook | Test Date | Sample Test |
Test 1 Solutions |
1.1 The Geometry and Algebra of Vectors 1.2 Length and Angle: The Dot Product 1.3 Lines and Planes Exploration: The Cross Product 2.1 Introduction to Systems of Linear Equations 2.2 Direct Methods for Solving Linear Systems 2.3 Spanning Sets and Linear Independence 2.4 Applications |
TBA | Sample Test 1Y Solutions Sample Test 1Z Solutions |
Test 2 Solutions |
3.1 Matrix Operations 3.2 Matrix Algebra 3.3 The Inverse of a Matrix 3.4 The LU Factorization 3.5 Subspaces, Basis, Dimension, and Rank 3.6 Introduction to Linear Transformations |
TBA | Sample Test 2Y Solutions Sample Test 2Z Solutions |
Test 3 Solutions |
Appendix C – Complex Numbers 4.1 Introduction to Eigenvalues and Eigenvectors 4.2 Determinants Exploration: Geometric Applications of Determinants 4.3 Eigenvalues and Eigenvectors of n×n Matrices 4.4 Similarity and Diagonalization 5.1 Orthogonality in R^{n} 5.2 Orthogonal Complements and Orthogonal Projections |
TBA | Sample Test 3Y Solutions Sample Test 3Z Solutions |
Remaining Sections: 5.3 The Gram-Schmidt Process and the QR Factorization 5.4 Orthogonal Diagonalization of Symmetric Matrices 7.3 Least Squares Approximation |
Final Exam
The MATH 251 final exam will be a comprehensive, three-hour exam and it will take place on sometime during the final exam period.
You must write the final exam at the scheduled time as per Camosun College's policy on final examinations.
Gilles Cazelais has provided a set of review questions along with solutions.
Pat Wrean has provided a practice exam along with solutions.
MATLAB, Octave and Other Software
- MATLAB
- GNU Octave (a free MATLAB clone)
- Octave Online (a free web-based UI for Octave)
- Linear Algebra with MATLAB (PDF handout created by Gilles Cazelais)
- Linear Algebra Toolkit
- Matrix Calculator
Links to other MATH 251 Webpages
Links to Textbook Resources from Publisher
Miscellaneous Links
- Right Hand Rule Graphic of the Cross Product (Exploration: The Cross Product)
- Geometric Interpretation of the Cross Product (Exploration: The Cross Product)
- Solutions of 3x3 Systems (3 Planes in R^{3}) (Sec 2.2)
Documents
- MATH 251 Course Outline for 2024W ("Official" syllabus is available for sec X03.)
- Properties of Vectors (Sec 1.1-1.2)
- Methane (Sec 1.2)
- Equations of Lines and Planes (Sec 1.3)
- Systems of Two Linear Equations in Two Variables (Sec 2.1)
- Row Echelon Form (Sec 2.2)
- Spanning Sets and Linear Independence of Vectors (Sec 2.3)
- Applications of Systems of Linear Equations (Sec 2.4)
- Properties of Matrices (Sec 3.2)
- Spanning Sets and Linear Independence of Matrices (Sec 3.2)
- Properties of Invertible Matrices (Sec 3.3)
- Elementary Matrices (Sec 3.3)
- Subspaces and Bases (Sec 3.5)
- Linear Transformations (Sec 3.6)
- Eigenvalues and Eigenvectors (Sec 4.1)
- Properties of Determinants (Sec 4.2)
- Diagonalization (Sec 4.4)
- Orthogonality (Sec 5.1-5.2)
- Gram-Schmidt Process (Sec 5.3)
- Symmetric Matrices and Orthogonal Diagonalization (Sec 5.4)
- Least Squares Approximation (Sec 7.3)