Course Description
In Mth.160 we introduce and discuss the following ideas:
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Introductory Material
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Systems of Linear Equations in Linear Algebra
- Coefficient and Augmented Coefficient Matrices
- The Elementary Operations, Row Reduction and Echelon Forms
- Solution Sets of Linear Systems
- Vectors and Vector Equations
- Introduction to Linear Transformations
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Matrix Algebra
- Matrix Operations
- Inverse of a Matrix
- Characterizations of Invertible Matrices
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Determinants
- An Introduction
- Properties of Determinants
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Vector Spaces
- Vector Spaces and Subspaces
- Null Spaces, Column Spaces, and Linear Transformations
- Linearly Independent Sets; Bases
- Coordinate Systems
- Dimension of a Vector Space
- Rank
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Eigenvectors and Eigenvalues
- Definitions
- The Characteristic Equation
- Diagonalization
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Orthogonality
- Inner Product, Length, and Orthogonality
- Orthogonal Sets
- Orthogonal Projections
- Least-Squares Problems
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Symmetric Matrices and Quadratic Forms
- Diagonalization of Symmetric Matrices
- Quadratic Forms