Description

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This text is designed for a one-semester introductory course in linear algebra. It uses Mathematica notebooks and packages to provide an interactive learning environment of experimentation, observation, and discussion. Contents

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Introduction to Mathematica | Introduction to Linear Systems and Row Operations | Linear Systems and Applications | Gaussian Elimination by Example | A Summary of Gaussian Elimination | Backsubstitution and Backaddition | Gaussian Elimination with Mathematica | The General Solution to Linear Systems | Matrix Multiplication from a Geometric Viewpoint | Matrix Arithmetic | Matrix Arithmetic with Mathematica | Properties of Matrix Algebra | Matrix Algebra and Block Matrices | Matrix Inverses: Definitions and Basic Properties | Computing Matrix Inverses | Elementary Matrices and the P(T)LU Decomposition | Applications of the P(T)LU Decomposition | Discovering Determinants | Systems of Equations from a Geometric Viewpoint | Vectors and Vector Spaces | Coordinate Systems and Bases | Independent and Spanning Sets | Constructing And Spanning Sets | Constructing Bases | The Theory of Bases | Subspaces and Linear Transformations | Inner Products | Orthonormal Bases and Projections | Gram-Schmidt Orthonormalization | Linear Transformations and Matrices | The Effects of Changing Coordinates | Discrete Dynamical Systems and Eigensystems | Eigenvectors and Eigenvalues | Appendix Related Topics

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Algebra