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MA 261

MA 261 -- Linear Algebra

  1. Systems of Linear Equations
    a) Introduction
    b) Gaussian Elimination and Gauss-Jordan Elimination

  2. Matrices
    a) Operations and properties
    b) Inverse of a matrix
    c) Elementary matrices

  3. Determinants
    a) The determinant of a matrix
    b) Evaluation of a determinant using elementary operations
    c) Properties

  4. Vector Spaces
    a) Vectors in Rn
    b) Vector spaces
    c) Subspaces of vector spaces
    d) Spanning sets and linear independence
    e) Basis and dimension
    f) Rank of a matrix and systems of linear equations
    g) Change of basis

  5. Inner Product Spaces
    a) Length and dot product in Rn
    b) Inner product spaces
    c) Orthonormal bases: Gram-Schmidt Process
    d) Mathematical models and Least Square Analysis

  6. Linear Transformations
    a) Introduction
    b) Kernel and range of a linear transformation
    c) Matrices for linear transformations
    d) Transition matrices and similarity

  7. Eigenvalues and Eigenvectors
    a) Introduction
    b) Diagonalization
    c) Symmetric matrices and orthogonal diagonalization

Learning Outcome 1: The student will demonstrate an understanding of elementary row operations and their applications.

Learning Outcome 2: The student will demonstrate an understanding of determinants, eigenvalues and eigenvectors.

Learning Outcome 3: The student will understand the basic theory of vector spaces involving linear maps between them, kernel and range, basis and dimension, and the construction of an orthonormal basis.