Math 346E: Elements of Linear Algebra, Spring 2017
Instructor: Sam van Gool
Monday & Wednesday, 2:003:15PM, NAC 6/122
Office hours as of May 3: Wednesday 11:0012:00, NAC 6/202A
Calendar
Note: This calendar will be kept up to date as the semester progresses.
# 
Date 
Section 
Contents 
Homework for next class 
1 
Mo 1/30 
1.1 
Course Introduction, Systems of Linear Equations 
Exercises: Section 1.1: 2, 6, 8, 10, 14, 16, 18, 20, 26, T/F Scan the entire course homepage 
2 
We 2/1 
1.2 
Gaussian Elimination 
Exercises: Section 1.2: 2, 4, 6, 10, 18, 26, 32, T/F Send an email to instructor (if you haven't already) 
3 
Mo 2/6 
1.3 
Matrices and Matrix Operations 
Exercises: Section 1.3: 4(a)(c), 5(a)&(b), 6(a)(c), 7(a)&(f), 12, 14, 19 Read: Section 1.4 Think about Method 4: ColumnRow Expansion 
4 
We 2/8 
1.4 
Inverses; Algebraic Properties of Matrices 
Exercises: Section 1.4: 2(c)&(d), 7, 8, 10, 20, 26, 40, T/F Read: Section 1.5 Remember: next class on Wednesday 2/15 
5 
We 2/15 
1.5 
Elementary Matrices and a Method for Finding A^1 
Exercises: Section 1.5: 4, 8, 14, 16, 18, 24, T/F Read: Section 1.6 Remember: next class on Wednesday 2/22 
6 
We 2/22 
1.6 
More on Linear Systems and Invertible Matrices 
Exercises: Section 1.6: 2, 6, 10, 12, 16, 20, 22, T/F Read: Section 1.7 Review: Sections 1.11.4 
7 
Mo 2/27 
1.7 
Diagonal, Triangular, and Symmetric Matrices 
Exercises: Section 1.7: 2, 4, 6, 12, 18, 20, 24, 36 Read: Section 2.1 Review: Chapter 1 entirely 
8 
We 3/1 
2.1 
Determinants by Cofactor Expansion 
Exercises: Section 2.1: 2, 4(a)&(b), 16, 20(a)&(f), 22, 32, T/F Read: Section 2.2 
9 
Mo 3/6 
2.2 & 2.3 
Evaluating Determinants by Row Reduction, Properties of Determinants; Cramer's Rule (statement) 
Exercises: Section 2.2: 6, 8, 12, 14, 16, 18, T/F AND Section 2.3: 8, 10, 18, 20, 22, 26, T/F Read: Section 2.3 
10 
We 3/8 
2.3 
Properties of Determinants; Cramer's Rule (proofs) 
Prepare for Midterm (no homework due on 3/13) 
11 
Mo 3/13 

MIDTERM EXAM 1 

12 
We 3/15 
3.1 
Vectors in 2Space, 3Space, and nSpace 
Exercises: Section 3.1: 2, 4, 8, 12, 16, 20, 22, T/F Read: Section 4.1 
13 
Mo 3/20 
4.1 
Real Vector Spaces 
Exercises: Section 4.1: 2, 4, 6, 8, 12, 14, 22, T/F Read: Section 4.2 
14 
We 3/22 
4.2 
Subspaces 
Exercises: Section 4.2: 2, 3, 4, 8(c), 10(a)&(b), 12, 15(a)&(b), 18, 22, T/F Read: Section 4.3 
15 
Mo 3/27 
4.3 
Linear Independence 
Exercises: Section 4.3: 2, 4, 10, 20, 25, 27, 29, 32, T/F Read: Section 4.4 
16 
We 3/29 
4.4 
Coordinates and Bases 
Exercises: Section 4.4: 2, 4, 7, 12, 14, 15, 19, 25, T/F Read: Section 4.5 and proof of Theorem 4.4.1 
17 
Mo 4/3 
4.5 
Dimension 
Exercises: Section 4.5: 2, 3, 7, 9, 10, 12, 14, 22, T/F Hand in: Proof of Theorem 4.5.2(b). Read: Section 4.6 
18 
We 4/5 
4.6 
Change of Basis 
Exercises: Section 4.6: 1, 3, 6, 9, 12, 15, 20, T/F Read: Section 4.7 Review: Sections 3.1, 4.14.6, and homework exercises for these sections 
19 
We 4/19 
4.7 
Row Space, Column Space, and Null Space 
Exercises: Section 4.7: 2, 3, 7, 10, 11, 16, 18, 24, T/F Read: Section 4.8 
20 
Th 4/20 
4.8 
Rank, Nullity, and the Fundamental Matrix Spaces 
Exercises: Section 4.8: 1, 4, 8, 10, 18, 21, 24, 28, T/F Read: Section 4.9 Send via email: a question for the review in next class 
21 
Mo 4/24 

Review 
Prepare for Midterm. No homework due on 4/26. 
22 
We 4/26 

MIDTERM EXAM 2 

23 
Mo 5/1 
1.8, 4.9, 5.1 
Matrix Transformations, Eigenvalues and Eigenvectors 
Exercises: Section 1.8: 2, 18. Section 4.9: 2, 6. Section 5.1: 2, 4, 6, 9, 20a,b, T/F Read: Section 5.1, 5.2 Office hour Wednesday 5/3, 1112. 
24 
We 5/3 
5.1, 5.2 
Eigenvalues and Eigenvectors (continued); Diagonalization 
Exercises: Section 5.1: 14, Section 5.2: 2, 4, 6, 8, 14, 16, 18, T/F Read: Section 8.1 
25 
Mo 5/8 
8.1 
General Linear Transformations 
Exercises: Section 8.1: 2, 6, 10, 12, 14, 20, 22, 24, 30, 31, T/F Read: Section 8.2 
26 
We 5/10 
8.2 
Compositions and Inverse Transformations 
Exercises: Section 8.2: 2, 4, 6, 12, 18, 20, 30, T/F; Section 8.3: 2, 4, 6, 8, 12, 14, T/F Read: Section 8.3 & 8.4 
27 
Mo 5/15 
8.3 & 8.4 
Isomorphism, Matrices for General Linear Transformations 
Exercises: Section 8.4: 2, 4, 8, 10, 18, T/F Review for final 
28 
We 5/17 
8.4 
Matrices for General Linear Transformations (continued); Review and Evaluation 
Two Homework sets for extra credit due 5/17: See PDF Review for final 

We 5/24 at 1:00PM 

FINAL EXAM 
See details below. 
Exams
Midterm exam 1: Monday March 13, 2:003:15, NAC 6/122
Midterm exam 2: Wednesday April 26, 2:003:15, NAC 6/122
Final exam: Wednesday May 24, 1:003:15, NAC 6/122
Additional Resources