Overview
Mathematics 271: Linear Algebra II continues the study of linear algebra from Mathematics 270. Mathematics 271 is suggested for students in the science programs. The course covers intermediate topics of linear algebra such as general vector spaces, eigenvalues and eigenvectors, inner product spaces, diagonalization and quadratic forms, and general linear transformations and applications of linear algebra.
Outline
Unit 1: General Vector Spaces
- Some of the topics covered in this unit are vector spaces; subspaces; linear independence; bases and dimension; change of basis; row, column and null spaces; rank and nullity; matrix transformations; and applications to computer graphics in 3D.
Unit 2: Eigenvalues and Eigenvectors
- Some of the topics covered in this unit are eigenvalues and eigenvectors; matrix diagonalization; and applications to genetics.
Unit 3: Inner Product Spaces
- Some of the topics covered in this unit are inner product spaces; orthogonality; Gram-Schmidt process; QR-decomposition; and method of least squares.
Unit 4: Diagonalization and Quadratic Forms
- Some of the topics covered in this unit are orthogonal matrices; orthogonal diagonalization; symmetric matrices; and applications of quadratic forms to conics.
Unit 5: General Linear Transformations
- Some of the topics covered in this unit are general linear transformations; composition and inverse of linear transformations; isomorphism; similarity; and applications to cryptography.
Learning outcomes
Upon successful completion of this course, you should be able to
- demonstrate understanding of general vector spaces, including concepts of subspace, linear independence of vectors, span, bases, change of bases, and dimension, as well as null, row and column spaces.
- find the bases for the eigenspaces of a matrix and understand their use in the process of diagonalizing a square matrix.
- demonstrate understanding of the concepts within general inner product spaces, including distance, orthogonality, orthogonal complement, and orthogonal projections, and apply these concepts to find the least squares polynomial fit to a given set of data points.
- apply the concepts of orthogonal diagonalization and symmetry to the study of quadratic forms and conics.
- demonstrate understanding of the concepts of linear transformations in general vector spaces, isomorphism and similarity; and their relationship to basic concepts of cryptography.
Evaluation
To receive credit for MATH 271, you must achieve a composite course grade of at least D (50 percent) and a grade of at least 50 percent on the final examination. The weighting of the composite grade is as follows:
Note: Calculators are not allowed during the examinations.
| Activity | Weight |
| 5 Assignments (3% each) | 15% |
| Midterm Exam | 35% |
| Final Exam | 50% |
| Total | 100% |
To learn more about assignments and examinations, please refer to Athabasca University’s online Calendar.
Materials
Digital course materials
Links to the following course materials will be made available in the course:
Anton, Howard, and Rorres, Chris.Elementary Linear Algebra: Applications Version (11th ed.). Hoboken, NJ: Wiley, 2014.
Anton, Howard, and Rorres, Chris. Elementary Linear Algebra: Applications Version, Student Solutions Manual (11th ed.). Hoboken, NJ: Wiley, 2014.
Other materials
The course materials include a Study Guide and Course Orientation.