
Systems of Linear Equations and Matrices 


1  (78) 

Introduction to Systems of Linear Equations 


1  (7) 


8  (17) 

Matrices and Matrix Operations 


25  (13) 

Inverses; Rules of Matrix Arithmetic 


38  (12) 

Elementary Matrices and a Method for Finding A1 


50  (9) 

Further Results on Systems of Equations and Invertibility 


59  (7) 

Diagonal, Triangular, and Symmetric Matrices 


66  (13) 


79  (38) 


79  (7) 

Evaluating Determinants by Row Reduction 


86  (6) 

Properties of the Determinant Function 


92  (9) 

Cofactor Expansion; Cramer's Rule 


101  (16) 

Vectors in 2Space and 3Space 


117  (50) 

Introduction to Vectors (Geometric) 


117  (10) 

Norm of a Vector; Vector Arithmetic 


127  (4) 


131  (10) 


141  (13) 

Lines and Planes in 3Space 


154  (13) 


167  (48) 


167  (14) 

Linear Transformations from Rn to Rm 


181  (18) 

Properties of Linear Transformations from Rn to Rm 


199  (16) 


215  (72) 


215  (7) 


222  (10) 


232  (9) 


241  (17) 

Row Space, Column Space, and Nullspace 


258  (14) 


272  (15) 


287  (68) 


287  (12) 

Angle and Orthogonality in Inner Product Spaces 


299  (13) 

Orthonormal Bases; GramSchmidt Process; QRDecomposition 


312  (16) 

Best Approximation; Least Squares 


328  (10) 

Orthogonal Matrices; Change of Basis 


338  (17) 

Eigenvalues, Eigenvectors 


355  (28) 

Eigenvalues and Eigenvectors 


355  (10) 


365  (10) 

Orthogonal Diagonalization 


375  (8) 


383  (58) 

General Linear Transformations 


383  (12) 


395  (7) 

Inverse Linear Transformations 


402  (8) 

Matrices of General Linear Transformations 


410  (14) 


424  (17) 


441  (80) 

Application to Differential Equations 


441  (7) 

Geometry of Linear Operators on R2 


448  (12) 

Least Squares Fitting to Data 


460  (7) 

Approximation Problems; Fourier Series 


467  (7) 


474  (9) 

Diagonalizing Quadratic Forms; Conic Sections 


483  (12) 


495  (5) 

Comparison of Procedures for Solving Linear Systems 


500  (10) 


510  (11) 


521  (50) 


521  (7) 

Modulus; Complex Conjugate; Division 


528  (7) 

Polar Form; DeMoivre's Theorem 


535  (9) 


544  (7) 

Complex Inner Product Spaces 


551  (8) 

Unitary, Normal, and Hermitian Matrices 


559  (12) 

Applications of Linear Algebra 


571  

Constructing Curves and Surfaces Through Specified Points 


571  (6) 


577  (3) 

Geometric Linear Programming 


580  (14) 


594  (9) 

Cubic Spline Interpolation 


603  (11) 


614  (11) 


625  (13) 


638  (9) 


647  (9) 


656  (9) 


665  (10) 

Equilibrium Temperature Distributions 


675  (10) 


685  (14) 


699  


617  (15) 


632  (112) 


744  (10) 

AgeSpecific Population Growth 


754  (10) 

Harvesting of Animal Populations 


764  (9) 

A Least Squares Model for Human Hearing 


773  
Answers to Exercises 

A1  (1) 
Insert Photo Credits 

P1  (1) 
Index 

I1  