Preface.Features of the Text.1. Systems of Linear Equations.1.1 The Vector Space of m x n Matrices.The Space R n .Linear Combinations and Linear Dependence.
What Is a Vector Space?Why Prove Anything?True-False Questions.Exercises.1.1.1 Computer Projects.Exercises.1.1.
2 Applications to Graph Theory I.Self-Study Questions.Exercises.1.2 Systems.Rank: The Maximum Number of Linearly Independent Equations.True-False Questions.Exercises.
1.2.1 Computer Projects.Exercises.1.2.2 Applications to Circuit Theory.Self-Study Questions.
Exercises.1.3 Gaussian Elimination.Spanning in Polynomial Spaces.Computational Issues: Pivoting.True-False Questions.Exercises.Computational Issues: Flops.
1.3.1 Computer Projects.Exercises.1.3.2 Applications to Traffic Flow.Self-Study Questions.
Exercises.1.4 Column Space and Nullspace.Subspaces.Subspaces of Functions.True-False Questions.Exercises.1.
4.1 Computer Projects.Exercises.1.4.2 Applications to Predator-Prey Problems.Self-Study Questions.Exercises.
Chapter Summary.2. Linear Independence and Dimension.2.1 The Test for Linear Independence.Bases for the Column Space.Testing Functions for Independence.True-False Questions.
Exercises.2.1.1 Computer Projects.2.2 Dimension.True-False Questions.Exercises.
2.2.1 Computer Projects.Exercises.2.2.2 Applications to Calculus.Self-Study Questions.
Exercises.2.2.3 Applications to Differential Equations.Self-Study Questions.Exercises.2.2.
4 Applications to the Harmonic Oscillator.Self-Study Questions.Exercises.2.2.5 Computer Projects.Exercises.2.
3 Row Space and the Rank-Nullity Theorem.Bases for the Row Space.Rank-Nullity Theorem.Computational Issues: Computing Rank.True-False Questions.Exercises.2.3.
1 Computer Projects.Chapter Summary.3. Linear Transformations.3.1 The Linearity Properties.True-False Questions.Exercises.
3.1.1 Computer Projects.3.1.2 Applications to Control Theory.Self-Study Questions.Exercises.
3.2 Matrix Multiplication (Composition).Partitioned Matrices.Computational Issues: Parallel Computing.True-False Questions.Exercises.3.2.
1 Computer Projects.3.2.2 Applications to Graph Theory II.Self-Study Questions.Exercises.3.3 Inverses.
Computational Issues: Reduction vs. Inverses.True-False Questions.Exercises.Ill Conditioned Systems.3.3.1 Computer Projects.
Exercises.3.3.2 Applications to Economics.Self-Study Questions.Exercises.3.4 The LU Factorization.
Exercises.3.4.1 Computer Projects.Exercises.3.5 The Matrix of a Linear Transformation.Coordinates.
Application to Differential Equations.Isomorphism.Invertible Linear Transformations.True-False Questions.Exercises.3.5.1 Computer Projects.
Chapter Summary.4. Determinants.4.1 Definition of the Determinant.4.1.1 The Rest of the Proofs.
True-False Questions.Exercises.4.1.2 Computer Projects.4.2 Reduction and Determinants.Uniqueness of the Determinant.
True-False Questions.Exercises.4.2.1 Application to Volume.Self-Study Questions.Exercises.4.
3 A Formula for Inverses.Cramer's Rule.True-False Questions.Exercises 273.Chapter Summary.5. Eigenvect.