Duke University
Department of Mathematics
Fall Semester, 2003
Mathematics 104.03: Linear Algebra and Applications

Course place and times: 113 Biological Sciences Building, Tuesdays and Thursdays, 2:15 - 3:30

Instructor:

Harold Layton
Fall 2003 Office Hours: Mondays 2:30-3:30, Wednesdays 4:00-5:00, and by appointment.
Office: Room 219B Physics Building, Science Drive, West Campus
Electronic mail: layton@math.duke.edu

Textbook:

Homework:

• Homework No. 1, due Thursday, August 28
Read Sections 1.1 (Vectors), 1.2 (Dot Product),
and 1.3 (Hyperplanes in Rn)
Problems to turn in:
Lesson 1, Pages 18-21: 3(a,c,e), 4, 5, 7, 15, 17, 18, 20, 21
• Homework No. 2, due Tuesday, September 2
Read Sections 1.4 (Systems of Linear Equations and Gaussian Elimination)
Problems to turn in:
Lesson 2, Pages 28-33: 1(a,e,g), 2(a,e,g), 3, 7, 10, 15, 17, 19
• Homework No. 3, due Thursday, September 4
Read Section 1.5 (Theory of Linear Systems)
Problems to turn in:
Lesson 3, Pages 41-43: 1(a,b,d), 3(a,b,c), 5, 7, 11 (problem 10 cancelled)
• Homework No. 4, due Tuesday, September 9
Problems to turn in:
Lesson 4, Pages 59-62: 1, 3(a--f), 4(b,c), 6, 7, 8
• For Thursday, September 11
and 2.1 (Matrix operations)
• Homework Nos. 6 and 7, due Tuesday, September 16
Problems to turn in:
Lessons 5 & 6, Pages 73-76: 1, 2(a,b), 3(a,b), 4a, 5b, 6, 8, 10, 12, 14
Lesson 7, Pages 89-92: 3, 5, 7, 8, 10, 11a, 12b
• Thursday, September 18
and Section 3.1 (Subspaces of Rn)
• Tuesday, September 23
Read Section 3.1 (Subspaces of Rn)
Problems to turn in:
Section 2.1: Pages 113-117: 1, 2(a,c,f), 6, 7(a,b,c,), 8, 9, 10(a,b,d), 11, 12, 13, 15, 19
Section 2.2: Pages 127-131: 1(a,b,d), 2(a,b,d), 4(a,c,d), 8, 10, 12, 13, 14, 15, 19
• Thursday, September 25
Problems to turn in:
Section 2.3: Pages 133-136: 1(a,j,k), 2, 3, 4, 5, 6, 7, 9, 13(a,b,c), 16, 17a
• Tuesday, September 30
Read Section 3.3 (Basis and Dimension)
Problems to turn in:
Section 3.1: Pages 152-155: 1(a,b,c,e,g), 2(a,b,c), 4, 6, 8(b,d), 9, 10, 12, 13(a,b), 16, 20
• Tuesday, October 7
Read Section 3.4 (The Four Fundamental Subspaces)
Problems to turn in:
Section 3.2: Pages: 165-167: 1, 2, 3(a,b), 4, 5, 6, 7, 11, 12, 14
• Thursday, October 9
Problems to turn in:
Section 3.3: Pages: 175-177: 1, 2(a,b,c), 3, 4(a,c), 6, 7, 10, 13, 14
• Thursday, October 16
Read Section 3.6 (Abstract Vector Spaces)
Problems to turn in:
Section 3.4: Pages: 188-191: 1(a,b,d), 4, 5, 7, 15, 16
• Tuesday, October 21
10-minute quiz (from Sections 3.1 -- 3.4)
Read Section 4.1 (Inconsistent Systems and Projection)
Problems to turn in:
Section 3.6: Pages: 211-214: 2(a,c,d), 3(a,c,f), 4, 6(a,b), 8, 11a, 12, 13(b,c), 14(a,b)
• Thursday, October 23
• Tuesday, October 28
Problems to turn in:
Section 4.1: Pages: 226-229: 1(a,b), 3, 4, 8, 9, 11
Section 4.2: Pages: 238-240: 2c, 3, 6, 7(a,b), 8a, 9a, 11, 12(a,b)
• Thursday, October 30
Read Section 4.4 (Change of Basis)
Problems to turn in:
Section 4.3: Pages: 252-256: 1, 3(a,c), 6, 9, 11, 13, 15, 17a.
• Tuesday , November 4
Read Sections 5.1 and 5.2 (Signed Area in Rn; Determinants)
Problems to turn in:
Section 4.4: Pages: 267-271: 1b, 3, 4, 14, 15, 16, 17
• Thursday, November 6
Major Quiz No. 2 (Chapter 3, except section 5; Chapter 4, Sections 1-3).
• Tuesday, November 11
Read Sections 5.3 and 6.1 (Cofactors and Cramer's Rule; The Characteristic Polynomial)
Problems to turn in:
Section 5.1: Pages: 278-279: 2, 3
Section 5.2: Pages: 287-290: 1(a,b,c), 2, 4, 5, 7, 9a, 11, 12
• Thursday, November 13
Problems to turn in:
Section 5.3: Pages: 298-301: 1, 2, 3, 5, 7, 8(a,c,f), 12a
• Tuesday, November 18
Read Section 6.4 (The Spectral Theorem)
• Thursday, November 20
Problems to turn in:
Section 6.1: Pages: 312-315: 1(a,b,d,g,h,i,p), 2, 3, 4, 6, 7(a,d), 9, 10, 13(a,b)
Section 6.2: Pages: 320-323: 1(a,b,d,g,h,i,p), 2(c,e,f), 4, 8, 11a, 12, 15, 18a
• Tuesday, November 25
Read Section 7.3 (Matrix Exponentials and Differential Equations)
Read Section 7.1 (Complex Eigenvalues and Jordan Canonical Form)
Problems to turn in:
Section 6.4: Pages: 345-349: 1(a,d,e,g), 3, 5, 7, 12(a,b,c,d), 16a, 17b
Section 7.3 (Part 1): Pages: 410-414: 7, 8a (for n = 3), 13a, 14 (prove for diagonalizable A only; for a hint, see page 311)
• Tuesday, December 2
Problems to turn in:
Section 7.3 (part 2): Pages: 410-414: 1(a,c,e), 2(a,b), 4, 5a, 6
Section 7.1 Pages: 366-370: 1, 2(a,c), 4, 13a
(problems 4 and 13a shouldn't require any new knowledge from Section 7.1)
• Thursday, December 4
Major Quiz No. 3 (Sections, 5.1, 5.2, 5.3, 6.1, 6.2, 6.4, 7.3)

Quizzes and Final Exam

• Major Quiz No. 1, Thursday, October 2
Chapters 1 and 2, inclusive. Closed book, closed notes.

• Quiz No. 2, Thursday, November 6
Chapters 3 and 4, except Sections 3.5 and 4.4. Closed book, closed notes.

• Quiz No. 3, Thursday, December 4
Sections 4.4, 5.1, 5.2, 5.3, 6.1, 6.2, 6.4, 7.3. Closed book, closed notes, no calculators.

• Final Exam, Friday, December 12, 2:00 - 5:00 in Room 113, Biological Sciences Building
Sections: all sections covered on Quizzes 1-3, plus sections 7.3 (part 2) and 7.1 (part 1). Closed book, closed notes, no calculators.