Anne Arundel Community College

MAT 202: Linear Algebra


CATALOG DESCRIPTION:
A study of finite-dimensional vector spaces. Topics include solutions of systems of linear equations; matrices (inverses, equivalence, rank of, symmetric, diagonal and orthogonal); determinants; introduction to vector spaces; linear independence; linear transformations; change of basis; eigenvalues and eigenvectors.

Prerequisite: MAT 191 or equivalent.

LEARNING OBJECTIVES:
Upon completion of this course, the student will be able to:
  1. Use matrix algebra to set up and solve systems of linear equations.
  2. Calculate determinants and apply them to understanding the nature of solutions to systems of linear equations and the existence of matrix inverses.
  3. Determine whether a given mathematical system satisfies the definition of a vector space.
  4. Use the concepts of a vector space to understand the nature of the solutions of a system of linear equations.
  5. Use linear transformations from one vector space to another with possible application to science and technology.
  6. Calculate eigenvalues and eigenvectors of linear transformations.
  7. Construct orthogonal bases on a vector space.

COURSE OUTLINE:
Systems of Linear Equations:
  • Introduction to Systems of Linear Equations
  • Gaussian Elimination and Gauss-Jordan Elimination
  • Applications of Systems of Linear Equations

Matrices:
  • Operations with Matrices
  • Properties of Matrix Operations
  • The Inverse of a Matrix
  • Elementary Matrices
  • Applications of Matrix Operations

Determinants:
  • The Determinant of a Matrix
  • Evaluation of a Determinant Using Elementary Operations
  • Properties of Determinants
  • Applications of Determinants

Vector Spaces:
  • Vectors in Rn
  • Vector Spaces
  • Subspaces of Vector Spaces
  • Spanning Sets and Linear Independence
  • Basis and Dimension
  • Rank of a Matrix and Systems of Linear Equations
  • Coordinates and Change of Basis

Inner Product Spaces:
  • Length and Dot Product in Rn
  • Inner Product Spaces
  • Orthonormal Bases: Gram-Schmidt Process (optional)

Linear Transformations:
  • Introduction to Linear Transformations
  • Kernel and Range of a Linear Transformation
  • Matrices for Linear Transformations
  • Transition Matrices and Similarity
  • Applications of Linear Transformations (optional)

Eigenvalues and Eigenvectors:
  • Eigenvalues and Eigenvectors
  • Diagonalization
  • Symmetric Matrices and Orthogonal Diagonalization
  • Applications of Eigenvalues and Eigenvectors

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