Linear Algebra

I.     Course Prefix/Number: MAT 260

       Course Name: Linear Algebra

       Credits: 3 (3 lecture; 0 lab)

II.    Prerequisite

MAT 251 with minimum grade of C.

III.   Course (Catalog) Description

Course covers matrices and the algebra of linear systems.  Content includes equations, vector spaces, real inner product spaces, linear transformations, determinants, eigenvalues, eigenvectors, diagonability, quadratic forms and symmetric matrices.  Calculators/computers used when appropriate.

IV.   Learning Objectives

1. Use basic matrix operations and the algebra of matrices to solve practical problems.  Applications include topics such as Kirchoff’s laws, the Leontieff model of an economy, Markov chains, least squares methods, singular value decomposition and Fourier coefficients of a function.
2. Determine if a set is a vector space or subspace.
3. Calculate bases, dimension and rank of a matrix, and use inner products to find lengths, projections, and angles between vectors.
4. Determine dependence and independence of a set of vectors.
5. Use the Gram-Schmidt process to find an orthogonal basis for a vector space.
6. Apply algebraic methods to construct, analyze and evaluate the following features of linear transformations:  their matrices, whether they are one-to-one or onto, their range and null spaces, and their similarity.
7. Apply properties of the determinant function, expand determinants using cofactors, and calculate determinants.
8. Calculate eigenvalues and eigenvectors.
9. Classify quadratic forms and find a basis for which a quadratic form has no cross-terms.

V.    Academic Integrity and Student Conduct


• cheating,
• falsification and fabrication (lying or distorting the truth),
• helping others to cheat,
• unauthorized changes on official documents,
• any other behavior that violates academic integrity.



VI.   Sequence of Topics

A.    Systems of Linear Equations and Matrices
    1     Gaussian elimination
    2     Homogeneous systems of linear equations
    3     Matrices and matrix arithmetic
    4     Matrix invertibility
    5      Applications

B.    Vector Spaces
    1.     Euclidean n-space
    2.     Linear independence
    3.     Basis and dimension
    4.     Rank of a matrix
    5.     Inner product spaces
    6.     Orthonormal bases and projections

C.    Linear Transformations
    1.     Properties, range and null space
    2.     Matrix representations, products and inverses
    3.     Similarity

D.    Determinants
    1.     The determinant function and evaluation
    2.     Properties of determinants        
    3.     Cofactor expansion        
    4.     Applications including Cramer's Rule
E.     Eigenvalues and Eigenvectors        
    1.     Eigenvalues and eigenvectors of linear transformations        
    2.     Diagonalization

F.     Quadratic forms
    1.    Symmetric matrices
G.    Recommended Technology
    1.    Use of technology to perform matrix computations
    2.    Use of technology to determine matrix products and inverses
    3.   Use of technology to evaluate determinants

VII.  Methods of Instruction

(To be completed by instructor)

Methods of presentation can include lectures, discussion, experimentation, audio-visual aids, small-group work and regularly assigned homework. Calculators/computers will be used when appropriate.  Mathematica, Derive, and TI-92 calculators are available for use at the College at no charge.

VIII. Course Practices Required

(To be completed by instructor)


IX.   Instructional Materials



Textbooks can also be found at our Mathematics Textbooks page.

X.    Methods of Evaluating Student Progress

(To be determined and announced by the instructor)


XI.   Other Course Information




Resources and support for
  • pregnancy-related and parenting accommodations; and
  • victims of sexual misconduct
can be found at

Resources and support for LGBTQ+ students can be found at