MA 261 -- Linear Algebra
- Systems of Linear Equations
a) Introduction
b) Gaussian Elimination and Gauss-Jordan Elimination - Matrices
a) Operations and properties
b) Inverse of a matrix
c) Elementary matrices - Determinants
a) The determinant of a matrix
b) Evaluation of a determinant using elementary operations
c) Properties - 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 - 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 - Linear Transformations
a) Introduction
b) Kernel and range of a linear transformation
c) Matrices for linear transformations
d) Transition matrices and similarity - 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.