Math 221 Introductory Linear Algebra. Topics covered in the course include the solution of systems of linear equations through Gaussian elimination; matrices and matrix algebra; vector spaces and their subspaces; coordinate mappings and other linear transformations; eigenvalues and eigenvectors; similarity and diagonalization; and constructions involving inner products such as orthogonal projections, the construction of Gram-Schmidt bases and least-square approximations. Although the course devotes a substantial amount of time to computational techniques, it should also lead the student to develop geometrical intuitions, to appreciate and understand mathematical abstraction, and to construct some elementary proofs.
Prerequisites: Math 100 with a minimum grade of 60%
Accessibility Services Notice
Students who would like an academic accommodation and who have a documented disability should contact Accessibility Services, if they have not already done so.Course Details| Total number of weeks | 15 |
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| Total Credits | |
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| Total Hours | 75 |
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Typical hours per week breakdown| Lecture | 3 |
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| Lab (lab, field, computer) | 2 |
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Learning Outcomes
Upon successful completion of this course, the learner will be able to:
- Apply Gaussian elimination, rank-nullity theorem, fundamental theorem of linear algebra, diagonalization algorithm, subspace test, coordinate transformations, row space algorithm, casting-out algorithm, Gram-Schmidt bases, and least-square approximations
- Define terms and concepts found in linear algebra
- Classify necessary and sufficient conditions for diagonalization, linear independence and dependence, subspaces, and matrix invertibility
- Construct elementary proofs
- Analyze parametric and vector equations and provide geometric descriptions for solutions to systems of linear equations
- Provide geometric descriptions for the kernel and image of linear transformations
Teaching and Learning Approach
Learning outcomes are achieved through studying examples and solving problems. Lectures are interactive, with
student participation encouraged and expected. Assessments provide opportunities to develop competence and
confidence with the theorems, algorithms, and examples that are introduced in lectures.
Students are responsible for regularly monitoring the course Moodle site for assessments, due dates, course
updates, and learning materials.Learning Resources
Textbook
Interactive Linear Algebra: UBC Edition
Dan Margalit, Joseph Rabinoff, Ben Williams
(Available online at no cost)
Online Assignments & Practice Platform
MathMatize.com
(Available online at no cost)Detailed Course Content, Topics, and Sequence Covered
1. Systems of Linear Equations
2. Matrix Algebra and Linear Systems
3. Invertible Matrices
4. Determinants
5. Vector Geometry
6. Cross Product and Complex Numbers
7. Winter Study Break College closed on Monday (Family Day). No classes for the week.
8. Linear Transformations
9. Eigenvalues and Eigenvectors
10. Subspaces
11. Span and Independence
12. Dimension and Bases
13. Gram-Schmidt and Orthogonality
14. Review
15. Final Exam PeriodAssessment
| Title | Learning Outcomes | Value |
|---|
| Online Quizzes (weekly) | 1-6 | 10% |
| In-Class Quizzes (weekly) | 1-6 | 10% |
| Assignments | 1-6 | 15% |
| Tests | 1-6 | 30% |
| Final Exam (1) | 1-6 | 35% |
| Total | 100% |
Grading Table
Standard Academic and Career Programs Grading Table
| Percentage |
Letter Grade |
GPA |
| 90-100 |
A+ |
4.33 |
| 85-89 |
A |
4.00 |
| 80-84 |
A- |
3.67 |
| 76-79 |
B+ |
3.33 |
| 72-75 |
B |
3.00 |
| 68-71 |
B- |
2.67 |
| 64-67 |
C+ |
2.33 |
| 60-63 |
C |
2.00 |
| 55-59 |
C- |
1.67 |
| 50-54 |
P |
1.00 |
| 0-49 |
F |
0.00 |
| |
DNW |
0.00 |
See the Academic Calendar for General Information including how to withdraw from course(s) and other regulations.
Disclaimer
Information contained in this course outline is correct at the time of publication. Content of the course is revised on an ongoing basis to ensure relevance to changing educational, employment and market needs. The instructor will endeavor to provide notice of changes to students as soon as possible. The instructor reserves the right to add or delete material from courses.