## Math 110: Linear Algebra (Fall 2010)

Description: Vector spaces. Linear transformations and matrices. Linear systems of equations. Determinants. Eigenvalues and eigenvectors. Inner product spaces. Self-adjoint, normal, and unitary maps. Course control number: 54239. Per-Olof Persson, persson@berkeley.edu, 1089 Evans, Phone (510) 642-6947 Office hours: Tue 9:30am - 11:00am and Fri 2:00pm - 3:30pm in 1089 Evans MWF 1-2pm, Room 100 Lewis S. H. Friedberg, A. J. Insel, and L. E. Spence, Linear Algebra, 4th edition, Prentice Hall, 2002 (Amazon). Lecture Slides, Chapter 1 - Vector Spaces (Full page, 6 per page) Lecture Slides, Chapter 2 - Linear Transformations and Matrices (Full page, 6 per page) Lecture Slides, Chapter 3 - Elementary Matrix Operations and Systems of Linear Equations (Full page, 6 per page) Lecture Slides, Chapter 4 - Determinants (Full page, 6 per page) Lecture Slides, Chapter 5 - Diagonalization (Full page, 6 per page) Lecture Slides, Chapter 6 - Inner Product Spaces (Full page, 6 per page) Notes on sets, logic, and mathematical language by Prof. George Bergman Solutions, problem 2.6.13 (a-b), from in-class office hours

Homework:
HW Date Problems Solutions
01 Wed 09/08 1.2: 1, 8, 10, 16, 19
1.3: 1, 3, 8ce, 13, 23, 30
1.4: 1, 2bf, 5aeg, 12, 15
PDF
02 Wed 09/15 1.5: 1, 2ef, 13, 17, 18
1.6: 1, 2abc, 3de, 14, 17, 22, 26, 31, 33
PDF
03 Wed 09/22 2.1: 1, 9, 11, 15, 18, 20, 26, 35
2.2: 1, 3, 10, 12, 13
PDF
04 Wed 09/29 2.3: 1, 3, 11, 13, 17
2.4: 1, 2, 6, 7, 9, 17
2.5: 1, 3ab, 6ab, 8, 10
PDF
05 Wed 10/13 2.6: 1, 4, 7, 14, 15
3.1: 1, 3, 5
PDF
06 Wed 10/20 3.2: 6, 14
3.3: 1, 2f, 3f
3.4: 1, 2ef, 10
4.1: 1
PDF
07 Wed 10/27 4.1: 9, 10
4.2: 1, 3, 12, 20, 23, 25, 26
4.3: 1, 10, 11, 14, 15, 23
PDF
08 Wed 11/03 4.4: 5, 6
5.1: 1, 3, 7, 9, 14, 17, 22
5.2: 1, 7, 8, 12, 13
PDF
09 Wed 11/17 5.3: 1, 2bdegi, 3, 4
5.4: 1, 3, 4, 5, 13, 17, 18
PDF
10 Wed 11/24 6.1: 1, 3, 9, 11, 17, 20
6.2: 1, 2abi, 13, 15
6.3: 1, 3, 12, 14
PDF
11 Wed 12/01 6.4: 1, 2, 12, 18
6.5: 1, 2, 15
PDF
Syllabus:
Lec Date Topic Other
01 Fri 08/27 1.2: Vector Spaces
02 Mon 08/30 1.3: Subspaces
03 Wed 09/01 1.4: Linear Combinations and Systems of Linear Equations
04 Fri 09/03 1.5: Linear Dependence and Linear Independence
Mon 09/06 Labor Day - No Lecture
05 Wed 09/08 1.6: Bases and Dimension HW1 Due
06 Fri 09/10 1.6: (cont'd)
07 Mon 09/13 2.1: Linear Transformations, Null Spaces, and Ranges
08 Wed 09/15 2.1: (cont'd) HW2 Due
09 Fri 09/17 2.2: The Matrix Representation of a Linear Transformation
10 Mon 09/20 2.3: Composition of Linear Transformations and Matrix Multiplication
11 Wed 09/22 2.4: Invertibility and Isomorphisms HW3 Due
12 Fri 09/24 2.4: (cont'd)
13 Mon 09/27 2.5: The Change of Coordinate Matrix
14 Wed 09/29 2.6: Dual Spaces HW4 Due
15 Fri 10/01 Review
16 Mon 10/04 Midterm 1 - In class, 100 Lewis, 1-2pm Midterm 1
17 Wed 10/06 3.1: Elementary Matrix Operations and Elementary Matrices
18 Fri 10/08 3.2: The Rank of a Matrix and Matrix Inverses
19 Mon 10/11 3.2: (cont'd)
20 Wed 10/13 3.3: Systems of Linear Equations - Theoretical Aspects HW5 Due
21 Fri 10/15 3.4: Systems of Linear Equations - Computational Aspects
22 Mon 10/18 4.1: Determinants of Order 2
23 Wed 10/20 4.2: Determinants of Order n HW6 Due
24 Fri 10/22 4.2: (cont'd)
25 Mon 10/25 4.3: Properties of Determinants
26 Wed 10/27 4.4: Summary - Important Facts about Determinants HW7 Due
27 Fri 10/29 5.1: Eigenvalues and Eigenvectors
28 Mon 11/01 5.2: Diagonalizability
29 Wed 11/03 5.3: Matrix Limits and Markov Chains HW8 Due
30 Fri 11/05 Review
31 Mon 11/08 Midterm 2 - In class, 100 Lewis, 1-2pm Midterm 2
32 Wed 11/10 5.4: Invariant Subspaces and the Cayley-Hamilton Theorem
33 Fri 11/12 5.4: (cont'd)
34 Mon 11/15 6.1: Inner Products and Norms
35 Wed 11/17 6.2: The Gram-Schmidt Orthogonalization Process and Orthogonal Complements HW9 Due
36 Fri 11/19 6.3: The Adjoint of a Linear Operator
37 Mon 11/22 6.4: Normal and Self-Adjoint Operators
38 Wed 11/24 6.4: (cont'd) HW10 Due
Fri 11/26 Thanksgiving - No lecture
39 Mon 11/29 6.5: Unitary and Orthogonal Operators and Their Matrices
40 Wed 12/01 Review HW11 Due
41 Fri 12/03 Review
Reading/Review/Recitation Week 12/6-12/10 - No lectures
Wed 12/15 Final Exam - 7-10pm Final Exam
GSIs and Discussion Sections:
Sec Time Room GSI E-mail Office Office hours
01 Wed 8am - 9am 87 Evans D. Penneys dpenneys@math.berkeley.edu 1049 Evans Tue 10-11am and 5-6pm, Wed 9-10am
02 Wed 9am - 10am 2032 Valley LSB C. Mitchell cmitch5@math.berkeley.edu 745 Evans Mon 2-4pm, Tue 1-2pm
03 Wed 10am - 11am B51 Hildebrand D. Beraldo beraldo@math.berkeley.edu 835 Evans Tue 4-6pm, Thu 4:30-5:30pm
04 Wed 11am - 12pm B51 Hildebrand D. Beraldo beraldo@math.berkeley.edu 835 Evans Tue 4-6pm, Thu 4:30-5:30pm
05 Wed 12pm - 1pm 75 Evans C. Mitchell cmitch5@math.berkeley.edu 745 Evans Mon 2-4pm, Tue 1-2pm
07 Wed 2pm - 3pm 87 Evans C. Mitchell cmitch5@math.berkeley.edu 745 Evans Mon 2-4pm, Tue 1-2pm
08 Wed 9am - 10am 3113 Etcheverry I. Ventura iventura@math.berkeley.edu 1039 Evans Tue 11:30am-1:30pm, Thu 4-6pm
09 Wed 2pm - 3pm 3 Evans D. Penneys dpenneys@math.berkeley.edu 1049 Evans Tue 10-11am and 5-6pm, Wed 9-10am
10 Wed 12pm - 1pm 310 Hearst I. Ventura iventura@math.berkeley.edu 1039 Evans Tue 11:30am-1:30pm, Thu 4-6pm