Robert Gardner's Online Linear Algebra

Online Linear Algebra
Solutions to Various Exercises Dr. Bob's Online University
(Not an actual university)
Robert 'Dr. Bob' Gardner

This website includes links to handwritten solutions to various exercises from John B. Fraleigh and Raymond A. Beauregard's Linear Algebra, 3rd edition, Addison-Wesley Publishing (1995). A few of the solutions are accompanied by YouTube videos.

Fraleigh and Beauregard's Linear Algebra book, 3rd edition

Robert "Dr. Bob" Gardner can be reached by e-mail at: gardnerr@etsu.edu. His office is in Gilbreath Hall, Room 308F on the ETSU campus.

Some videos of lectures are available on the Online Linear Algebra with online videos webpage.

Chapter 1. Vectors, Matrices, and Linear Systems.

SECTION	NOTES	SUPPLEMENTS	SOLUTIONS
1.1. Vectors in Euclidean Spaces	1.1 Notes	1.1 Supplement 1.1 Supplement Print File	Exercise 1.1.19 Exercise 1.1.25 Exercise 1.1.27 Exercise 1.1.30 Exercise 1.1.31
1.2. The Norm and Dot Product	1.2 Notes	1.2 Supplement 1.2 Supplement Print File	Exercise 1.2.23 Exercise 1.2.37 Exercise 1.2.39 Exercise 1.2.43
1.3. Matrices and Their Algebra	1.3 Notes	1.3 Supplement 1.3 Supplement Print File	Exercise 1.3.19 Exercise 1.3.37 Exercise 1.3.39 Exercise 1.3.45
1.4. Solving Systems of Linear Equations	1.4 Notes	1.4 Supplement 1.4 Supplement Print File	Exercise 1.4.9 Exercise 1.4.15 Exercise 1.4.17 Exercise 1.4.23 Exercise 1.4.24 Exercise 1.4.25
1.5. Inverses of Square Matrices	1.5 Notes	1.5 Supplement 1.5 Supplement Print File	Exercise 1.5.15 Exercise 1.5.17 Exercise 1.5.25 Exercise 1.5.27 Exercise 1.5.29 Exercise 1.5.31 Exercise 1.5.37
1.6. Homogeneous Systems, Subspaces, and Bases	1.6 Notes	1.6 Supplement 1.6 Supplement Print File	Exercise 1.6.5 Exercise 1.6.25 Exercise 1.6.31 Exercise 1.6.33
1.7. Application to Population Distributions	1.7 Notes	1.7 Supplement 1.7 Supplement Print File	-

Chapter 2. Dimension, Rank, and Linear Transformations.

SECTION	NOTES	SUPPLEMENTS	SOLUTIONS
2.1. Independence and Dimension	2.1 Notes	2.1 Supplement 2.1 Supplement Print File	Exercise 2.1.5 Exercise 2.1.13 , Video (8:08) Exercise 2.1.23 , Video (5:40) Exercise 2.1.29 Exercise 2.1.33 Exercise 2.1.35 Exercise 2.1.37
2.2. The Rank of a Matrix	2.2 Notes	2.2 Supplement 2.2 Supplement Print File	Exercise 2.2.3 Exercise 2.2.5 , Video Part 1 (6:06), Video Part 2 (9:33) Exercise 2.2.7 Exercise 2.2.13 Exercise 2.2.15 Exercise 2.2.17 Exercise 2.2.19 Exercise 2.2.21
2.3. Linear Transformations of Euclidean Spaces	2.3 Notes	2.3 Supplement 2.3 Supplement Print File	Exercise 2.3.5 Exercise 2.3.15 Exercise 2.3.17 Exercise 2.3.19 , Video (11:35) Exercise 2.3.23 Exercise 2.3.25 Exercise 2.3.33
2.4. Linear Transformations of the Plane	2.4 Notes	2.4 Supplement 2.4 Supplement Print File	Exercise 2.4.17 Exercise 2.4.19 Exercise 2.4.21
2.5. Lines, Planes, and Other Flats	2.5 Notes	2.5 Supplement 2.5 Supplement Print File	Exercise 2.5.9 Exercise 2.5.11(c) Exercise 2.5.19 Exercise 2.5.37 , Video (7:02) Exercise 2.5.38

Chapter 3. Vector Spaces.

SECTION	NOTES	SUPPLEMENTS	SOLUTIONS
3.1. Vector Spaces	3.1 Notes	3.1 Supplement 3.1 Supplement Print File	Exercise 3.1.1 Exercise 3.1.23 Exercise 3.1.25 Exercise 3.1.27 Exercise 3.1.29
3.2. Basic Concepts of Vector Spaces	3.2 Notes	3.2 Supplement 3.2 Supplement Print File	Exercise 3.2.1 Exercise 3.2.5 Exercise 3.2.21 , Video (12:36) Exercise 3.2.23 Exercise 3.2.31 Exercise 3.2.33 Exercise 3.2.37 Exercise 3.2.39 Exercise 3.2.41 Exercise 3.2.43 Exercise 3.2.45
3.3. Coordinatization of Vectors	3.3 Notes	3.3 Supplement 3.3 Supplement Print File	Exercise 3.3.5 , Video (6:10) Exercise 3.3.9 , Video (10:59) Exercise 3.3.10 Exercise 3.3.19
3.4. Linear Transformations	3.4 Notes	3.4 Supplement 3.4 Supplement Print File	Exercise 3.4.5 Exercise 3.4.39 Exercise 3.4.41 Exercise 3.4.45 Exercise 3.4.47 Exercise 3.4.49 Exercise 3.4.51
3.5. Inner-Product Spaces	3.5 Notes	3.5 Supplement 3.5 Supplement Print File	Exercise 3.5.17 Exercise 3.5.19 Exercise 3.5.27

Chapter 4. Determinants.

SECTION	NOTES	SUPPLEMENTS	SOLUTIONS
4.1. Areas, Volumes, and Cross Products	4.1 Notes	4.1 Supplement 4.1 Supplement Print File	Exercise 4.1.11 Exercise 4.1.13 , Video (6:24) Exercise 4.1.27 , Video (9:32) Exercise 4.1.29 Exercise 4.1.57 Exercise 4.1.59
4.2. The Determinant of a Square Matrix	4.2 Notes	4.2 Supplement 4.2 Supplement Print File	Exercise 4.2.1 , Video (6:45) Exercise 4.2.3 Exercise 4.2.13 , Video (6:41) Exercise 4.2.19 Exercise 4.2.29 , Video (6:29) Exercise 4.2.33 Exercise 4.2.35
4.3. Computation of Determinants and Cramer's Rule	4.3 Notes	4.3 Supplement 4.3 Supplement Print File	Exercise 4.3.3 , Video (6:24) Exercise 4.3.4 Exercise 4.3.31 , Video (9:09) Exercise 4.3.37 Exercise 4.3.39
4.4. Linear Transformations and Determinants	4.4 Notes	4.4 Supplement 4.4 Supplement Print File

Chapter 5. Eigenvalues and Eigenvectors.

SECTION	NOTES	SUPPLEMENTS	SOLUTIONS
5.1. Eigenvalues and Eigenvectors	5.1 Notes	5.1 Supplement 5.1 Supplement Print File	Exercise 5.1.11 , Video (24:35) Exercise 5.1.15 Exercise 5.1.17 Exercise 5.1.25 Exercise 5.1.27 Exercise 5.1.29 Exercise 5.1.35 Exercise 5.1.41
5.2. Diagonalization	5.2 Notes	5.2 Supplement 5.2 Supplement Print File	Exercise 5.2.5 , Video (21:16) Exercise 5.2.11 , Video (7:00) Exercise 5.2.17 Exercise 5.2.19 Exercise 5.2.21 Exercise 5.2.23 Exercise 5.2.25 Exercise 5.2.27
5.3. Two Applications	5.3 Notes	5.3 Supplement 5.3 Supplement Print File

Chapter 6. Eigenvalues and Eigenvectors.

SECTION	NOTES	SUPPLEMENTS	SOLUTIONS
6.1. Projections	6.1 Notes	6.1 Supplement 6.1 Supplement Print File	Exercise 6.1.11 , Video (11:05) Exercise 6.1.15 , Video (20:34) Exercise 6.1.25 Exercise 6.1.27 Exercise 6.1.39
6.2. The Gram-Schmidt Process	6.2 Notes	6.2 Supplement (PDF) 6.2 Supplement Print File (PDF)	Exercise 6.2.9 , Video (20:33) Exercise 6.2.11 Exercise 6.2.29 Exercise 6.2.31 Exercise 6.2.33 Exercise 6.2.35
6.3. Orthogonal Matrices	6.3 Notes	6.3 Supplement 6.3 Supplement Print File	Exercise 6.3.25 Exercise 6.3.27 Exercise 6.3.29 Exercise 6.3.31 Exercise 6.3.39 Exercise 6.3.41
6.4. The Projection Matrix	6.4 Notes	6.4 Supplement 6.4 Supplement Print File	-
6.5. The Method of Least Squares	6.5 Notes	6.5 Supplement 6.5 Supplement Print File	-

Additional notes and supplements based on Fraleigh and Beauregard's Linear Algebra are available on the Linear Algebra Class Notes webpage.

Return to Dr. Bob's webpage

Last updated: May 11, 2024.