***This is a course guideline. Students should contact instructor for the updated information on current course syllabus, textbooks, and course content***
Text: Linear Algebra and Its Applications (5th Edition) [Hardcover], David C. Lay. ISBN: 9780321982384
Prerequisite: Credit for or concurrent enrollment in MATH 1432.
Course Description: Solutions of systems of linear equations, matrices, vector spaces, linear transformations, similarity eigenvalues and eigenvectors. *Note: TCCNS Equivalent: MATH 2318
(1) Linear Equations in Linear Algebra
1.1 Systems of Linear Equations
1.2 Row Reduction and Solution Sets of Linear Systems
1.3 Vector Equations
1.4 The Matrix Equation Ax =b
1.5 Solutions Sets of Linear Systems
1.7 Linear Independence
1.8 Introduction to Linear Transformations
1.9 The Matrix of a Linear Transformation
(2) Matrix Algebra
2.1 Matrix Operations
2.2-3 The Inverse of a Matrix and Characterizations of Invertibility
2.4 Partitioned Matrices
2.8 Subspaces of R^n
2.9 Dimension and Rank
3.3 Cramer's Rule, Volume, and Linear Transformations
*Permutation Matrices (not in text)
*Sections are optional, as time permits
(4) Vector Spaces
4.1 Vector Spaces and Subspaces
4.2 Null Spaces, Column Spaces, and Linear Transformations
4.3 Linearly Independent Sets; Bases
*4.4 Coordinate Systems
4.5 The Dimension of Vector Space
*4.7 Change of Basis
*4.9 Applications to Markov Chains
(5) Eigenvalues and Eigenvectors
5.1 Eigenvectors and Eigenvalues
5.2 The Characteristic Equation
*5.4 Eigenvectors and Linear Transformations
*5.5 Complex Eigenvalues
(6) Orthogonality and Symmetric Matrices
6.1 Inner Product, Length, and Orthogonality
6.3 Orthogonality and Projections
6.4 The Gram-Schmidt Process
6.5 Least-Squares Problems
(7) Symmetric Matrices and Quadratic Forms
*7.1 Diagonalization of Symmetric Matrices
*7.2 Quadratic Forms
*7.3 The Singular Value Decomposition
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