Section

Topic

page

Suggested Exercises

1.1

Introduction to systems of linear equations

6

1,4,5,7,10,11-13

1.2

Gaussian elimination

19

1,3,4,6,10,12,17,18,22,25,26,31,32

1.3

Matrices and matrix operations

34

1,3,5,6,7,12,15,16,17,20,22,27-30

1.4

Inverses; rules of matrix arithmetic

48

1,3,5,6,7,14-17,29,31,35

1.5

Elementary matrices and a method for finding A^-1

57

1-6,19,20

1.6

Further results on systems of equations, invertibility

66

1,5,11

2.1

Determinants by cofactor expansion

94

1-4,11,12,15

2.2

Evaluating determinants by row reduction

101

1,3,5,9

2.3

Properties of the determinant function

109

2,4,5,12,16,18,20-23

2.4

A combinatorial approach to determinants

117

1,2,4,5,7,10,17

4.1

Euclidean n-space

178

1,3,4,5,8-11,14-17,23,37

4.2

Linear transformations from Rⁿ to R^m

193

2,3,5,6,9,12,15,17,19,21

4.3

Properties of linear transformations from Rⁿ to R^m

206

1,3,5,8-11,13,15,21,22,25

5.1

Real vector spaces

226

1-12,25

5.2

Subspaces

238

1,3-9,11,14,15,23

5.3

Linear independence

248

1,2,3,7,9,15,24

5.4

Basis and dimension

263

1-4,7-9,11,13,15,17

5.5

Row space, column space, and null space

276

1,2,3,5,6,9,11,15

5.6

Rank and nullity

288

1,2,4,7,13,17

7.1

Eigenvalues and eigenvectors

367

1-6,11,16,20,24

7.2

Diagonalization

378

1,2,3,5,9,11,13,19,20,25

8.1

General linear transformations

398

1,3-10,13,15,17,19,31,33

8.2

Kernel and range

405

1,3,5,7,8,11,12,16,17,21,25

8.3

Inverse linear transformations

413

1-4,7,9,12,13,22

8.4

Matrices of general linear transformations

426

1,3,5,6,9,13,16

8.5

Similarity

439

1,3,5,11,12,19