Elementary Linear Algebra Student Solutions, Fourth Edition : Used with ... Larson-Elementary Linear Algebra

by Larson

• ISBN13: 9780395967195
• ISBN10: 0395967198
• Edition: 4th
• Format: Paperback
• Copyright: 1999-07-09
• Publisher: Brooks Cole

Table of Contents

Systems of Linear Equations
Introduction to Systems of Linear Equations	1	(12)
Gaussian Elimination and Gauss-Jordan Elimination	13	(10)
Applications of Systems of Linear Equations	23	(16)
Review Exercises	32	(7)
Matrices
Operations with Matrices	39	(7)
Properties of Matrix Operations	46	(6)
The Inverse of a Matrix	52	(8)
Elementary Matrices	60	(6)
Applications of Matrix Operations	66	(20)
Review Exercises	77	(9)
Determinants
The Determinant of a Matrix	86	(7)
Evaluation of a Determinant Using Elementary Operations	93	(4)
Properties of Determinants	97	(6)
Applications of Determinants	103	(30)
Review Exercises	117	(12)
Chapters 1-3 Cumulative Test	129	(4)
Vector Spaces
Vectors in Rn	133	(6)
Vector Spaces	139	(3)
Subspaces of Vector Spaces	142	(3)
Spanning Sets and Linear Independence	145	(8)
Basis and Dimension	153	(4)
Rank of a Matrix and Systems of Linear Equations	157	(6)
Coordinates and Change of Basis	163	(5)
Applications of Vector Spaces	168	(19)
Review Exercises	178	(9)
Inner Product Spaces
Length and Dot Product in Rn	187	(7)
Inner Product Spaces	194	(8)
Orthonormal Bases: Gram-Schmidt Process	202	(11)
Mathematical Models and Least Squares Analysis	213	(5)
Applications of Inner Product Spaces	218	(27)
Review Exercises	230	(11)
Chapters 4-5 Cumulative Test	241	(4)
Linear Transformations
Introduction to Linear Transformations	245	(5)
The Kernel and Range of a Linear Transformation	250	(5)
Matrices for Linear Transformations	255	(16)
Transition Matrices and Similarity	271	(4)
Applications of Linear Transformations	275	(16)
Review Exercises	281	(10)
Eigenvalues and Eigenvectors
Eigenvalues and Eigenvectors	291	(10)
Diagonalization	301	(6)
Symmetric Matrices and Orthogonal Diagonalization	307	(3)
Applications of Eigenvalues and Eigenvectors	310	(8)
Review Exercises	318	(7)
Chapters 6-7 Cumulative Test	325