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MATH 321 LINEAR ALGEBRA

Catalog Description: Systems of linear equations, matrices and determinants. Vector spaces and linear transformations.
Eigenvalues, eigenvectors, diagonalization of a symmetric matrix.
Prerequisites : Math 135 and Math 152 with grade of C or higher.

Textbook: Elementary Linear Algebra, 6th edition, by Larson, Edwards, and Falvo.

Course Outline and Topics

Chapter 1: Systems Of Linear Equations
1.1: Introduction to Systems of Linear Equations
1.2: Gaussian Elimination and Gauss -Jordan Elimination
1.3: Applications of Systems of Linear Equations

Chapter 2: Matrices
2.1: Operations with Matrices
2.2: Properties of Matrix Operations
2.3: The Inverse of a Matrix
2.4: Elementary Matrices

Chapter 3: Determinants
3.1: The Determinant of a Matrix
3.2: Evaluation of a Determinant Using Elementary Operations
3.3: Properties of Determinants
3.4: Introduction to Eigenvalues

Chapter 4: Vector Spaces
4.1: Vectors in Rn
4.2: Vector Spaces
4.3: Subspaces of Vector Spaces
4.4: Spanning Sets and Linear Independence
4.5: Basis and Dimension
4.6: Rank of a Matrix and Systems of Linear Equations
4.7: Coordinates and Change of Basis

Chapter 5: Inner Product Spaces
5.1: Length and Dot Product in R n
5.2: Inner Product Spaces
5.3: Orthonormal Bases: Gram-Schmidt Process

Chapter 6: Linear Transformations
6.1: Introduction to Linear Transformations
6.2: The Kernel and Range of a Linear Transformation
6.3: Matrices for Linear Transformations
6.4: Transition Matrices and Similarity

Chapter 7: Eigenvalues And Eigenvectors
7.1: Eigenvalues and Eigenvectors
7.2: Diagonalization
7.3: Symmetric Matrices and Orthogonal Diagonalization

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