MATH 251 - Matrix Algebra for Engineers

Announcements

Apr 7: This is a reminder that Saturday, April 13 is the last day you can withdraw from most Winter 2024 courses (including MATH 251) without academic penalty.

Feb 17: The Winter 2024 final exam schedule has been posted on myCamosun (click here for a direct link to the schedule). See below for details of the MATH 251 final exam.

Feb 14: There are no classes during the week of February 19-23 due to the Family day holiday on Monday followed by Reading Break. Office hours are cancelled that week. Please email me if you have any questions. The Math Lab (E224) will be open with regular hours on Tuesday, Wednesday and Thursday of Reading Break.

Jan 11: This is a reminder that Sunday, January 14 is the deadline for adding courses or dropping courses with an 80% tuition refund.

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.

Assignments are due before 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 Thursday, January 25
Assignment 2 Solutions 2.1, 2.2, 2.3, 2.4 Monday, February 5
Assignment 3 Solutions 3.1, 3.2, 3.3 Tuesday, February 13
Assignment 4 Solutions 3.4, 3.5, 3.6 Tuesday, March 5
Assignment 5 Solutions App. C, 4.1, 4.2, Expl. Determinants Monday, March 18
Assignment 6 Solutions 4.3, 4.4, 5.1, 5.2 Tuesday, April 2
Assignment 7 Solutions 5.3, 5.4, 7.3 Thursday, April 11

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		 Friday, February 9 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		 Friday, March 8 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 Rn
5.2 Orthogonal Complements and Orthogonal Projections
 Friday, April 5 Sample Test 3Y
Solutions

Sample Test 3Z
Solutions
Final 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 Friday, April 19 from 8:30-11:30am in Young 217/219.

You must write the final exam at the scheduled time as per Camosun College's policy on final examinations.

Exam Period Office Hours (E260):

I may be contacted by email (ballinger@camosun.ca) at other times. 

You will be provided with the rotation matrix and the least squares solution formula:

Final Exam Formulas

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