Catalog Description: 
Systems of linear equations, vector spaces, linear independence, basis, dimension, linear transformations, matrices, determinants,
eigenvalues, and geometric applications. (Offered every semester.)

Prerequisites: 
MATH 112 Calculus II with a C or better or the instructor's consent

Required Course Materials: 
Howard Anton, Elementary Linear Algebra, 10^{th} edition,
Wiley, 2010 (ISBN: 9780479458211)

Course Coordinator: 
Lamarr C. Widmer, Ph.D., Professor of Mathematics

Course Audience: 
Information Science, Engineering and Mathematics majors and Mathematics minors.

Course Objectives: 
 To develop a rigorous understanding of the foundational ideas of linear algebra.
 Develop facility in standard computations with matrices, linear systems and vector calculations.
 To enhance comprehension by examining geometric interpretations of the foundational concepts.
 To select and use technology (i.e. calculator or computer software) when appropriate in problem solving.
 To develop an ability to recognize linear algebra concepts in the context of mathematical problems and applications and implement the corresponding processes.
 To develop the process of making appropriate conjectures, finding suitable means to test those conjectures and drawing conclusions about their validity.

Topics: 
 Linear systems: systems of linear equations with
solution by row reduction, homogeneous systems
 Matrices: matrix operations, properties of matrix arithmetic, matrix inverse relationship of invertibility
of matrix to solubility of system
 Determinants: the determinant function, relationship of
determinant and row reduction, properties of the
determinant, cofactor expansion
 Vector Spaces: Euclidean spaces R^{2}
and R^{3}, axiomatic definition of vector
space, subspaces, linear independence, basis, dimension,
rank and nullity
 Inner Product Spaces: Axiomatic definition of inner product space, angle and orthogonality, orthonormal
basis, GramSchmidt process
 Eigenvalues and eigenvectors: definition and geometric meaning of
eigenvalues and eigenvectors, characteristic equation, diagonalization
of a matrix
 Linear transformations: axiomatic definition of linear
transformation, kernel and range, inverse transformations,
linear transformations of Euclidean spaces

