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

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




Assignment 1: Unit 1 8%
Assignment 2: Unit 2 8%
Assignment 3: Unit 3 8%
Assignment 4: Unit 4 8%
Assignment 5: Unit 5 8%
Final examination * 60%
Total 100%

* Mandatory

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