Transcript title

Topics in Linear Algebra

Credits

1

Grading mode

Standard letter grades

Total contact hours

10

Lecture hours

10

Prerequisites

MTH 112Z or higher (except MTH 211, MTH 212, MTH 213, MTH 244, and STAT 243Z) or minimum placement Math Level 22.

Recommended preparation

MTH 261A.

Course Description

Provides additional topics in linear algebra for students taking MTH 261A, Introduction to Linear Algebra. Topics include: using technology to row-reduce matrices, find inverses, calculate determinants, eigenvalues and eigenvectors; using determinants and the rank-nullity theorem to investigate solution sets and matrix invertibility; vector spaces and subspaces; and diagonalization and the eigenvector problem.

Course learning outcomes

1. Use technology to perform matrix computations including row-reduction, finding inverses, and calculating determinants, eigenvalues and eigenvectors.
2. Draw conclusions about the solution sets of linear equations and the invertibility of matrices using determinants and the rank-nullity theorem.
3. Investigate topics in vector spaces including: determining whether a subset is a subspace, determining a basis and dimension of a given subspace, including the null space and column space of a matrix and the eigenspaces of square matrices.
4. Investigate the relationship between the eigenvector problem and diagonalization.

Content outline

1. Introduction to technology
   1. row-reduction computation
   2. finding inverses
   3. calculating determinants
   4. eigenvalues and eigenvectors
2. Cramer's Rule
3. Rank-nullity Theorem
4. Definition of a subspace
5. Determine a basis and dimension of a given subspace
   1. null space
   2. column space
   3. eigenspaces
6. Diagonalization
   1. performing calculation
   2. relationship to the eigenvector problem

Required materials

No required materials.