Elementary Linear Algebra: A Matrix Approach
Exercises

This page lists exercises corresponding to the first edition of our textbook, for students who wish to use that edition. The sections correspond very closely, but not exactly, to the second edition.

Spence1E

First edition:

Elementary Linear Algebra: A Matrix Approach, by Lawrence E. Spence, Arnold J. Insel, and Stephen H. Friedberg. Prentice Hall, 2000. ISBN-10: 0137167229, ISBN-13: 9780137167227. AddALL ($42 and up).


Exercises

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 first edition of our textbook.

Section Exercises
1.1 Matrices and Vectors1-16
1.2 Linear Combinations, Matrix-Vector Products, and Special Matrices1-32
1.3 Systems of Linear Equations1-38
1.4 Gaussian Elimination1-32
1.6 The Span of a Set of Vectors1-36
1.7 Linear Dependence and Linear Independence1-34
2.1 Matrix Multiplication1-21
2.3 Invertibility and Elementary Matrices1-16
2.4 The Inverse of a Matrix1-22
2.6 Linear Transformations and Matrices1-34
2.7 Composition and Invertibility of Linear Transformations1-58
Exam 1
3.1 Cofactor Expansion1-40
3.2 Properties of Determinants1-36
4.1 Subspaces1-50
4.2 Basis and Dimension1-34
4.3 The Dimension of Subspaces Associated with a Matrix1-34
4.4 Coordinate Systems1-24
4.5 Matrix Representations of Linear Operations1-30
5.1 Eigenvalues and Eigenvectors1-36
5.2 The characteristic Polynomial1-54
5.3 Diagonalization of Matrices1-34
5.4 Diagonalization of Linear Operators1-26
Exam 2
6.1 The Geometry of Vectors1-29
6.2 Orthogonal Vectors1-28
6.3 Least-Squares Approximation and Orthogonal Matrices and Operators1-22
6.4 Orthogonal Matrices and Operators1-16
6.5 Symmetric Matrices1-20
7.1 Vector Spaces and their Subspaces1-11
7.2 Dimension and Isomorphism1-26
7.3 Linear Transformations and Matrix Representations1-10
7.4 Inner Product Spaces1-17
Final