MATH 251 - Matrix Algebra for Engineers


None at this time.

Lecture Notes

In case they prove helpful, on D2L ( 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.

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
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

Sample Test 1Z
Test 2
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

Sample Test 2Z
Test 3
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 Rn
5.2 Orthogonal Complements and Orthogonal Projections
TBA Sample Test 3Y

Sample Test 3Z
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

Links to other MATH 251 Webpages

Links to Textbook Resources from Publisher

Miscellaneous Links

Documents PDF