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Linear Algebra and Its Applications, 5th Edition Linear Algebra and Its Applications, 5th Edition

Chapter 1

Linear Equations In Linear Algebra

	Systems of Linear Equations	Exercises	p
	Row Reduction and Echelon Forms	Exercises	p
	Vector Equations	Exercises	p
	The Matrix Equation Ax=b	Exercises	p
	Solution Sets of Linear Systems	Exercises	p
	Applications of Linear Systems	Exercises	p
	Linear Independence	Exercises	p
	Introduction to Linear Transformations	Exercises	p
	The Matrix of a Linear Transformation	Exercises	p
	Linear Models in Business, Science, and Engineering	Exercises	p
Supplementary Exercises	p

Chapter 2

Matrix Algebra

	Matrix Operations	Exercises	p
	The Inverse of a Matrix	Exercises	p
	Characterizations of Invertible Matrices	Exercises	p
	Partitioned Matrices	Exercises	p
	Matrix Factorizations	Exercises	p
	The Leontief Input-Output Model	Exercises	p
	Applications to Computer Graphics	Exercises	p
	Subspaces of R^n	Exercises	p
	Dimension and Rank	Exercises	p
Supplementary Exercises	p

Chapter 3

Determinants

	Introduction to Determinants	Exercises	p
	Properties of Determinants	Exercises	p
	Cramer's Rule, Volume, and Linear Transformations	Exercises	p
Supplementary Exercises	p

Chapter 4

Vector Spaces

	Vector Spaces and Subspaces	Exercises	p
	Null Spaces, Column Spaces, and Linear Transformations	Exercises	p
	Linearly Independent Sets; Bases	Exercises	p
	Coordinate Systems	Exercises	p
	The Dimension of a Vector Space	Exercises	p
	Rank	Exercises	p
	Change of Basis	Exercises	p
	Applications to Difference Equations	Exercises	p
	Applications to Markov Chains	Exercises	p
Supplementary Exercises	p

Chapter 5

Eigenvalues And Eigenvectors

	Eigenvectors and Eigenvalues	Exercises	p
	The Characteristic Equation	Exercises	p
	Diagonalization	Exercises	p
	Eigenvectors and Linear Transformations	Exercises	p
	Complex Eigenvalues	Exercises	p
	Discrete Dynamical Systems	Exercises	p
	Applications to Diferential Equations	Exercises	p
	Iterative Estimates for Eigenvalues	Exercises	p
Supplementary Exercises	p

Chapter 6

Orthogonality And Least Squares

	Inner Product, Length, and Orthogonality	Exercises	p
	Orthogonal Sets	Exercises	p
	Orthogonal Projections	Exercises	p
	The Gram-Schmidt Process	Exercises	p
	Least-Squares Problems	Exercises	p
	Applications to Linear Models	Exercises	p
	Inner Product Spaces	Exercises	p
	Applications of Inner Product Spaces	Exercises	p
Supplementary Exercises	p

Chapter 7

Symmetric Matrices And Quadratic Forms

	Diagonalization of Symmetric Matrices	Exercises	p
	Quadratic Forms	Exercises	p
	Constrained Optimization	Exercises	p
	The Singular Value Decomposition	Exercises	p
	Applications to Image Processing and Statistics	Exercises	p
Supplementary Exercises	p

Chapter 8

The Geometry Of Vector Spaces

Affine Combinations	Exercises	p
Affine Independence	Exercises	p
Convex Combinations	Exercises	p
Hyperplanes	Exercises	p
Polytopes	Exercises	p
Curves and Surfaces	Exercises	p

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Introduction to linear algebra 5th pdf download