# MATH 2121: Linear Algebra

Students explore the following topics: systems of linear equations, matrix arithmetic, determinants, real vector spaces, linear transformations, eigenvalues, eigenvectors, and diagonalization.

## Learning outcomes

• Solve systems of linear equations and homogeneous systems of linear equations by Gaussian elimination and Gauss-Jordan elimination.
• Row-reduce a matrix to either row-echelon or reduced row-echelon form.
• Use matrix operations to solve systems of equations and be able to determine the nature of the solutions.
• Understand some applications of systems of linear equations.
• Perform operations with matrices and find the transpose and inverse of a matrix.
• Calculate determinants using row operations, column operations and expansion down any column and across any row.
• Interpret vectors in two and three-dimensional space both algebraically and geometrically.
• Use the Gram-Schmidt process to produce an orthonormal basis.
• Use basic mathematical proof techniques to prove or disprove certain claims (e.g. prove or disprove whether a given set of objects constitutes a vector space).
• Find the kernel, range, rank, and nullity of a linear transformation.
• Calculate eigenvalues and their corresponding eigenspaces.
• Understand the concept of a linear transformation as a mapping from one vector space to another and be able to calculate its matrix representation with respect to standard and nonstandard bases.
• Determine if a matrix is diagonalizable, and if it is, how to diagonalize it.

## Course topics

• Unit 1: Systems of Linear Equations
• Unit 2: Matrices and Determinants
• Unit 3: Vector Spaces
• Unit 4: Inner Product Spaces
• Unit 5: Linear Transformations, Eigenvalues and Eigenvectors

## Required text and materials

The following materials are required for this course:

1. Larson, R. (2017). Elementary linear algebra (8th ed.). Boston, MA: Brooks/Cole, Cengage Learning.
Type: Textbook ISBN: 978-1-305-65800-4
1. Larson, R. (2017). Student solutions manual for elementary linear algebra (8th ed.). Boston, MA: Brooks/Cole, Cengage Learning.
Type: Textbook ISBN: 978-1-305-65802-8

## Optional materials

A scientific calculator is allowed both in the course term work and on the final exam. Graphing calculators are not permitted.