
Systems of Linear Equations and Matrices 


1  (81) 

Introduction to Systems of Linear Equations 


2  (6) 


8  (15) 

Matrices and Matrix Operations 


23  (14) 

Inverses; Rules of Matrix Arithmetic 


37  (13) 

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  (15) 


81  (38) 


82  (7) 

Evaluating Determinants by Row Reduction 


89  (6) 

Properties of the Determinant Function 


95  (9) 

Cofactor Expansion; Cramer's Rule 


104  (15) 

Vectors in 2Space and 3Space 


119  (42) 

Introduction to Vectors (Geometric) 


120  (6) 

Norm of a Vector; Vector Arithmetic 


126  (4) 


130  (8) 


138  (11) 

Lines and Planes in 3Space 


149  (12) 


161  (42) 


162  (11) 

Linear Transformations from Rn to Rm 


173  (16) 

Properties of Linear Transformations from Rn to Rm 


189  (14) 


203  (72) 


204  (7) 


211  (10) 


221  (10) 


231  (15) 

Row Space, Column Space, and Nullspace 


246  (13) 


259  (16) 


275  (62) 


276  (11) 

Angle and Orthogonality in Inner Product Spaces 


287  (11) 

Orthonormal Bases; GramSchmidt Process; QRDecomposition 


298  (13) 

Best Approximation; Least Squares 


311  (9) 

Orthogonal Matrices; Change of Basis 


320  (17) 

Eigenvalues, Eigenvectors 


337  (28) 

Eigenvalues and Eigenvectors 


338  (9) 


347  (10) 

Orthogonal Diagonalization 


357  (8) 


365  (54) 

General Linear Transformations 


366  (10) 


376  (6) 

Inverse Linear Transformations 


382  (8) 

Matrices of General Linear Transformations 


390  (12) 


402  (17) 


419  (68) 

Application to Differential Equations 


420  (6) 

Geometry of Linear Operators on R2 


426  (11) 

Least Squares Fitting to Data 


437  (5) 

Approximation Problems; Fourier Series 


442  (5) 


447  (7) 

Diagonalizing Quadratic Forms; Conic Sections 


454  (9) 


463  (5) 

Comparison of Procedures for Solving Linear Systems 


468  (9) 


477  (10) 


487  (44) 


488  (6) 

Division of Complex Numbers 


494  (6) 

Polar Form of a Complex Number 


500  (6) 


506  (7) 

Complex Inner Product Spaces 


513  (7) 

Unitary, Normal, and Hermitian Matrices 


520  (11) 
Answers to Exercises 

531  (48) 
Photo Credits 

579  (2) 
Index 

581  