MATH461 summer 2011 - course webpage

Office hours: 11am-1pm weekdays in MATH3303
Tutoring hours: 12:30-2:30pm weekdays in room MATH0303
My email: sonlam at math dot umd dot edu

Hi linear algebraists, this is your course webpage. Here you will find the syllabus, course materials, and a list of exercises. I will update the exercise list as we move along the course, so check back frequently. As a rule, always read the relevant sections in the text before attempting the exercises.

Exercise List

From Linear Algebra w/ applications - 3rd edition - David Lay
1.4: 7,15,21,25,27,31
1.5: 11,25,27,39,40,26
1.7: 3,7,15,19,20,33,35,37,39
4.1: 5,9,11,25,33,35
1.8: 1,3,7,17,19,21,23,29
1.9: 1,3,15,29,30,31,32,35(keywords:"one-to-one", "onto")
2.1: 1,5,13,21,25,31
2.2: 1,11,13,18,21,23 (look back to 1.9.31), 24 (look back to 1.9.32)
2.3: (Assume square matrices for these exercises)15,17,19,23,25,27,29,31,37
2.5: 21,25,26
2.8: 1,2,3,4,13,27,33,35
4.2: 1,3,7,13,29,35
4.3: 1,2,7,9,23,25,31(read carefully: dependent vs independent)
4.4: 1,5,19,23,24,25
4.5: 1,9,21,25(read theorem 12),27,29,31(do not work with matrices for this question, W may be infinite dimensional)
Hint for 31: First show that if {h1,...,hn} is basis for H then {T(h1),...,T(hn)} span T(H).
4.6: Read "Invertible matrix theorem (continued)", 1,5,9,13,19,25,31,32,33,34
Email me if you have questions about 31-34 above.
4.7: 1,13,15
3.1: 1,25,26,27,28,29,30,37
3.2: 29,31,32,33,34,35(you can use the fact that U transpose and U have same determinant),36
5.1: (Review how to find a basis for Nul A) 1,9,11,15,19,23,24,25,26,27,31,35
5.2: 3,9,17,19,23
5.3: 1,11,13,17,21(be careful with true false questions),25,27,29,31
5.4: 1
5.5: 1,13,25
Read 5.6
6.1: 1,3,5,9,13,24 (hint: use definition of "length" in terms of dot product),27,29 (use theorem 1)
6.2: 2,11,13,15,17,25,27,29,32
6.3: 3,7,11,15,20
6.4: 9,11,22
6.5: 1,3,19,22
6.6: 1

Course materials:
Syllabus
Resources
How to study
Guidelines on proofs
Quiz 1
Quiz 2
Project 1
Quiz 3
Quiz 4
Project 2

Testbank
Sample exam 1 - (our exam will be longer: less True/False, more proofs. In our exam, vectors will have arrows on top) Solution

Announcements:
- Final exam is on Friday Aug 19.
- The final will be cumulative, but computations will be more focused on 5.5, chapter 6 and 7. - Cheat sheet will be provided with all the theorems needed. You will have to memorize and understand all definitions.
- Office hours in 3303.