
Systems of Linear Equations and Matrices 


1  (82) 

Introduction to Systems of Linear Equations 


2  (6) 


8  (15) 

Matrices and Matrix Operations 


23  (16) 

Inverses; Rules of Matrix Arithmetic 


39  (12) 

Elementary Matrices and a Method for Finding A1 


51  (9) 

Further Results on Systems of Equations and Invertibility 


60  (8) 

Diagonal, Triangular, and Symmetric Matrices 


68  (15) 


83  (40) 

Determinants by Cofactor Expansion 


84  (12) 

Evaluating Determinants by Row Reduction 


96  (7) 

Properties of the Determinant Function 


103  (8) 

A Combinatorial Approach to Determinants 


111  (12) 

Vectors in 2Space and 3Space 


123  (44) 

Introduction to Vectors (Geometric) 


124  (7) 

Norm of a Vector; Vector Arithmetic 


131  (5) 


136  (8) 


144  (12) 

Lines and Planes in 3Space 


156  (11) 


167  (54) 


168  (13) 

Linear Transformations from Rn to Rm 


181  (16) 

Properties of Linear Transformations from Rn to Rm 


197  (13) 

Linear Transformations and Polynomials 


210  (11) 


221  (74) 


222  (7) 


229  (11) 


240  (10) 


250  (16) 

Row Space, Column Space, and Nullspace 


266  (13) 


279  (16) 


295  (64) 


296  (11) 

Angle and Orthogonality in Inner Product Spaces 


307  (11) 

Orthonormal Bases; GramSchmidt Prodcess; Q RDecomposition 


318  (14) 

Best Approximation; Least Squares 


332  (9) 


341  (6) 


347  (12) 

Eigenvalues, Eigenvectors 


359  (30) 

Eigenvalues and Eigenvectors 


360  (9) 


369  (11) 

Orthogonal Diagonalization 


380  (9) 


389  (62) 

General Linear Transformations 


390  (10) 


400  (7) 

Inverse Linear Transformations 


407  (9) 

Matrices of General Linear Transformations 


416  (14) 


430  (12) 


442  (9) 


451  (70) 

Application to Differential Equations 


452  (6) 

Geometry of Linear Operators on R2 


458  (10) 

Least Squares Fitting to Data 


468  (6) 

Approximation Problems; Fourier Series 


474  (5) 


479  (8) 

Diagonalizing Quadratic Forms; Conic Sections 


487  (10) 


497  (5) 

Comparison of Procedures for Solving Linear Systems 


502  (9) 


511  (10) 


521  (46) 


522  (6) 

Division of Complex Numbers 


528  (5) 

Polar Form of a Complex Number 


533  (7) 


540  (7) 

Complex Inner Product Spaces 


547  (7) 

Unitary Normal, and Hermitian Matrices 


554  (13) 

Applications of Linear Algebra 


567  (212) 

Constructing Curves and Surfaces through Specified Points 


568  (6) 


574  (4) 

Geometric Linear Programming 


578  (12) 

The Earliest Applications of Linear Algebra 


590  (7) 

Cubic Spline Interpolation 


597  (11) 


608  (11) 


619  (10) 


629  (10) 


639  (9) 


648  (9) 


657  (8) 

Equilibrium Temperature Distributions 


665  (11) 


676  (12) 


688  (17) 


705  (14) 


719  (13) 


732  (11) 

AgeSpecific Population Growth 


743  (10) 

Harvesting of Animal Populations 


753  (9) 

A Least Squares Model for Human Hearing 


762  (6) 


768  (11) 
Answers to Exercises 

779  (44) 
Index 

823  