Mathematics (MATH) 271

Linear Algebra II (Revision 6)

MATH 271

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Mathematics Diagnostic Assessment. This online test contains 70 questions that will help you assess your mathematical skills. Based on your score we will recommend which Athabasca University mathematics course you are likely ready to take successfully.

Delivery Mode: Individualized study online (with eTextbook)

Credits: 3

Area of Study: Science

Prerequisite: MATH 270

Faculty: Faculty of Science & Technology

Centre: Centre for Science

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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.


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.


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:

Activity Weighting
5 Assignments (3% each) 15%
Midterm Exam 35%
Final Exam 50%
Total 100%

Note: Calculators are not allowed during the examinations.

To learn more about assignments and examinations, please refer to Athabasca University's online Calendar.

Course Materials


Registration in this course includes an electronic textbook. For more information on electronic textbooks, please refer to our eText Initiative site.

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.

A print version of the eText may be available for purchase from the publisher through a direct-to-student link provided on the course website; you can also acquire the textbook on your own if you wish.

Other materials

The course materials include a Study Guide and Course Orientation.

Athabasca University reserves the right to amend course outlines occasionally and without notice. Courses offered by other delivery methods may vary from their individualized-study counterparts.

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Opened in Revision 6, Nov 9, 2018.

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