This page lists exercises corresponding to the second edition of our textbook, for students who wish to use that edition. The sections correspond very closely, but not exactly, to the first edition.
Elementary Linear Algebra, 2/E, by Lawrence E. Spence, Arnold J. Insel, and Stephen H. Friedberg. Prentice Hall, 2008. ISBN-10: 0131871412, ISBN-13: 9780131871410. University bookstore ($130) or AddALL ($70 and up).
Exercises are not collected. Below, I am listing all exercises that you certainly should be able to solve. Use your judgment in deciding which exercises to actually work. It is a good idea to work as many exercises as you can find time to solve; your goal is to achieve fluency, so that you can complete exams comfortably in the time allowed.
You are also invited to look at the more advanced exercises that are not listed.
The following exercises are for the second edition of our textbook.
| Section | Exercises |
| 1.1 Matrices and Vectors | 1-32 |
| 1.2 Linear Combinations, Matrix-Vector Products, and Special Matrices | 1-44 |
| 1.3 Systems of Linear Equations | 1-54 |
| 1.4 Gaussian Elimination | 1-42 |
| 1.6 The Span of a Set of Vectors | 1-44 |
| 1.7 Linear Dependence and Linear Independence | 1-62 |
| 2.1 Matrix Multiplication | 1-32 |
| 2.3 Invertibility and Elementary Matrices | 1-32 |
| 2.4 The Inverse of a Matrix | 1-34 |
| 2.7 Linear Transformations and Matrices | 1-34 |
| 2.8 Composition and Invertibility of Linear Transformations | 1-40 |
| Exam 1 | |
| 3.1 Cofactor Expansion | 1-44 |
| 3.2 Properties of Determinants | 1-38 |
| 4.1 Subspaces | 1-42 |
| 4.2 Basis and Dimension | 1-32 |
| 4.3 The Dimension of Subspaces Associated with a Matrix | 1-40 |
| 4.4 Coordinate Systems | 1-30 |
| 4.5 Matrix Representations of Linear Operations | 1-18 |
| 5.1 Eigenvalues and Eigenvectors | 1-40 |
| 5.2 The characteristic Polynomial | 1-40 |
| 5.3 Diagonalization of Matrices | 1-28 |
| 5.4 Diagonalization of Linear Operators | 1-28 |
| Exam 2 | |
| 6.1 The Geometry of Vectors | |
| 6.2 Orthogonal Vectors | |
| 6.3 Orthogonal Projections | |
| 6.4 Least-Squares Approximations and Orthogonal Projections | |
| 6.5 Orthogonal Matrices and Operators | |
| 6.6 Symmetric Matrices | |
| 7.1 Vector Spaces and their Subspaces | |
| 7.2 Linear Transformations | |
| 7.3 Basis and Dimension | |
| 7.4 Matrix Representations of Linear Operators | |
| 7.5 Inner Product Spaces | |
| Final |