9781256873211

Linear Algebra & Differential Equations (Custom Edition for University of California, Berkeley)

David C. Lay, Nagle, Saff, Snider

2nd Edition

Suitable for Math 54 at UC Berkeley.I also have the student study guide, which is optional and sold separately.

1.1

Systems of Linear Equations

Exercises

p.12

1.2

Row Reduction and Echelon Forms

Exercises

p.23

1.3

Vector Equations

Exercises

p.34

1.4

The Matrix Equation Ax=b

Exercises

p.42

1.5

Solution Sets of Linear Systems

Exercises

p.49

1.6

Applications of Linear Systems

Exercises

p.56

1.7

Linear Independence

Exercises

p.62

1.8

Introduction to Linear Transformations

Exercises

p.70

1.9

The Matrix of a Linear Transformation

Exercises

p.80

1.10

Linear Models in Business, Science, and Engineering

Exercises

p.88

Supplementary Exercises

p.90

2.1

Matrix Operations

Exercises

p.102

2.2

The Inverse of a Matrix

Exercises

p.111

2.3

Characterizations of Invertible Matrices

Exercises

p.117

2.4

Partitioned Matrices

Exercises

p.123

2.5

Matrix Factorizations

Exercises

p.131

2.6

Subspaces of R^n

Exercises

p.139

2.7

Dimension and Rank

Exercises

p.145

Supplementary Exercises

p.148

4.1

Vector Spaces and Subspaces

Exercises

p.183

4.2

Null Spaces, Column Spaces, and Linear Transformations

Exercises

p.193

4.3

Linearly Independent Sets; Bases

Exercises

p.201

4.4

Coordinate Systems

Exercises

p.210

4.5

The Dimension of a Vector Space

Exercises

p.217

4.6

Rank

Exercises

p.224

4.7

Change of Basis

Exercises

p.230

Supplementary Exercises

p.232

4.1

Introduction: The Mass-Spring Oscillator

Exercises

p.399

4.2

Homogeneous Linear Equations: The General Solution

Exercises

p.407

4.3

Auxiliary Equations with Complex Roots

Exercises

p.415

4.4

Nonhomogeneous Equations: The Method of Undetermind Coefficients

Exercises

p.424

4.5

The Superposition Principle and Undetermined Coefficients and Nonlinear Equations

Exercises

p.429

4.6

Variation of Parameters

Exercises

p.435

4.7

Qualitative Considerations for Variable-Coefficient and Nonlinear Equations

Exercises

p.444

4.8

A Closer Look at Free Mechanical Vibrations

Exercises

p.454

4.9

A Closer Look at Forced Mechanical Vibrations

Exercises

p.462

Review Problems

p.465

6.1

Inner Product, Length, and Orthogonality

Exercises

p.282

6.2

Orthogonal Sets

Exercises

p.290

6.3

Orthogonal Projections

Exercises

p.298

6.4

The Gram-Schmidt Process

Exercises

p.304

6.5

Least-Squares Problems

Exercises

p.312

6.6

Applications to Linear Models

Exercises

p.320

6.7

Inner Product Spaces

Exercises

p.328

6.8

Applications of Inner Product Spaces

Exercises

p.335

Supplementary Exercises

p.336

9.1

Introduction

Exercises

p.503

9.2

Review 1: Linear Algebraic Equations

Exercises

p.507

9.3

Review 2: Matrices and Vectors

Exercises

p.516

9.4

Linear Systems in Normal Form

Exercises

p.524

9.5

Homogeneous Linear Systems with Constant Coefficients

Exercises

p.535

9.6

Complex Eigenvalues

Exercises

p.542

9.7

Nonhomogeneous Linear Systems

Exercises

p.548

9.8

The Matrix Exponential Function

Exercises

p.558

Review Problems

p.562

Technical Writing Exercises

p.563