Week 1


March 25

 Introduction, vector spaces
 Read Section 1.2
 Homework: pp. 13  16: 4bf, 8, 10, 12, 15, 21 (only show associativity)

March 27

 Subspaces, fields
 Read Section 1.3 and skim Appendix C
 Homework: pp. 20  22: 2dfh, 5, 10, 11, 20, 23, 25

March 29

 Linear combination and linear equations
 Read Section 1.4
 Homework: pp. 33  34: Use the method of Section 1.4 to solve these equations, 2bd, 4c, 6, 8, 10

Week
2


April 1

 Linear dependence and independence
 Read Section 1.5
 Homework: pp. 40  42: 2ac, 5, 6, 9, 17, 18

April 3 
 Bases and dimension
 Read Section 1.6 (skip Lagrange interpolation)
 Homework: pp. 54  55: 2d, 3e, 4, 7, 11, 12

April 5 
 Bases and dimension
 Read Section 1.6 (skip Lagrange interpolation)
 Homework: pp. 55  57: 13, 16, 20, 23, 29

Week
3


April 8 
 Linear Transformations
 Read Section 2.1
 Homework: pp. 74  75: 3, 5  7, 10

April 10 
 Linear Transformations
 Read Section 2.1
 Homework: pp. 75  78: 14ac, 17, 21, 28, 38

April 12 
 Matrix representation of a linear transformation
 Read Section 2.2
 Homework: pp. 84  85: 2bd, 3, 4, 5c, 8

Week
4


April 15

 Composition of linear transformations and matrix multiplication (skip Applications)
 Read Section 2.3
 Homework: pp. 96  97: 2b, 3, 11

April 17 
 Composition of linear transformations and matrix multiplication (skip Applications); Invertability and
isomorphisms
 Read Sections 2.3 and 2.4
 Homework: pp. 97  98: 12, 13; pp. 106  107: 2de, 10

April 18

 Xhour, 12:00  12:50
 First midterm exam: inclass portion

April 19 
 Invertability and
isomorphisms
 Read Section 2.4
 Homework: p. 108: 16, 17, 20

Week
5


April 22 
 Change of coordinate matrix
 Read Section 2.5
 Homework: pp. 116  118: 1, 2c, 3c, 4, 9  11

April 24 
 No class today. Classes canceled at Dartmouth.

April 25 
 Class held today during xhour.
 Homework Week 4 due today
 Elementary operations and elementary matrices
 Read Section 3.1
 Homework: pp. 151  152: 2, 3ac, 8, 9

April 26 
 The rank of a matrix and matrix inverses
 Read Section 3.2
 Homework: pp. 165  166: 2acf, 4ab

Week
6


April 29 
 The rank of a matrix and matrix inverses
 Read Section 3.2
 Homework: pp. 166  168: 5ab, 6cd, 8, 15

May 1 
 Homework Week 5 due today
 Systems of linear equations Theory (skip An Application)
 Read Section 3.3
 Homework: pp. 179  181: 2dg, 3dg, 7ad, 8b, 9, 10

May 3

 Systems of linear equations  Computations (up to p. 193)
 Read Section 3.4
 Homework: pp. 195  197: 2abf, 5 (Hint: Thm 3.16), 7, 9

Week
7


May 6

 Determinants (Definitions, facts and examples)
 Read Section 4.4
 Homework: pp. 236  238: 2d, 3dg, 4de, 5 (induction?)

May 8 
 Homework 6 due today covering assignments made on
5/1, 5/3 and 5/6
 Eigenvalues and eigenvectors
 Read Section 5.1
 Homework: pp. 256  260: 2c, 3ad, 8ab, 14  16

May 10 
 Diagonalizability (up to and including p. 271)
 Read Section 5.2
 Homework: pp. 280  281: 3ce, 11, 12

Week
8


May 13

 Diagonalizability Continued (up to and including p. 271)
 Read Section 5.2
 Homework: none

May 15 
 Homework 7 due today covering assignments made on 5/8 and 5/10
 Inner products and norms
 Read: Section 6.1
 Homework: pp. 336  338: 2, 3, 10, 11, 15a, 17, 20a

May 16

 Xhour, 12:00  12:50
 Second midterm exam: inclass portion

May 17

 The GramSchmidt process and orthogonal complements
 Read: Section 6.2
 Homework: pp. 353  354: 2acd, 4, 11, 12

Week
9


May 20

 The adjoint of a linear operator
 Read: Section 6.3 (Skip Least Squares Approximation)
 Homework (Assigned but will not be collected): pp. 366  367: 3b, 6, 8, 10, 11

May 22 
 Normal and selfadjoint operators
 Read: Section 6.4
 No Homework

May 24 
 Homework 8 due today covering assignments made on 5/15 and 5/17
 Unitary and orthogonal operators
 Read: Section 6.5
 No Homework

Week
10


May 27


May 29

 LAST CLASS
 Questions, Comments, Discussion of Final Exam, etc.
