MATH 261 Linear Algebra (3)

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, 10th edition, Wiley, 2010 (ISBN: 978-0-479-45821-1)

 

Course Coordinator:

Lamarr C. Widmer, Ph.D., Professor of Mathematics


Course Audience:

Information Science, Engineering and Mathematics majors and Mathematics minors.


Course Objectives:

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

Topics:

  1. Linear systems: systems of linear equations with solution by row reduction, homogeneous systems
  2. Matrices: matrix operations, properties of matrix arithmetic, matrix inverse relationship of invertibility of matrix to solubility of system
  3. Determinants: the determinant function, relationship of determinant and row reduction, properties of the determinant, cofactor expansion
  4. Vector Spaces: Euclidean spaces R2 and R3, axiomatic definition of vector space, subspaces, linear independence, basis, dimension, rank and nullity
  5. Inner Product Spaces: Axiomatic definition of inner product space, angle and orthogonality, orthonormal basis, Gram-Schmidt process
  6. Eigenvalues and eigenvectors: definition and geometric meaning of eigenvalues and eigenvectors, characteristic equation, diagonalization of a matrix
  7. Linear transformations: axiomatic definition of linear transformation, kernel and range, inverse transformations, linear transformations of Euclidean spaces

 

Reviewed May 2012; Revised September 2011

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