MTH 513  Fall
2007 Linear Algebra Meets TR:
5:006:15 – 106 Instructor: Dr. Nancy Eaton Email me: eaton@math.uri.edu Wednesday 912
or by appointment


Students who require
accommodations and who have documentation from
Disability Services (8742098) should make arrangements
with me as soon as possible.


Course Content
Principle topics
of linear algebra are covered. Vector
spaces are emphasized along with linear transformations and their relationship
to matrices. Topics are selected from
the following list
1. Vector Spaces. NotesCh1P1
NotesCh1P2
Ø
Introduction. Vector Spaces. Subspaces. Linear
Combinations and Systems of Linear Equations. Linear Dependence and Linear
Independence. Bases and Dimension. Maximal Linearly Independent Subsets.
2. Linear Transformations and Matrices.
Notes
Ø
Linear Transformations, Null Spaces, and Ranges. The
Matrix Representation of a Linear Transformation. Composition of Linear
Transformations and Matrix Multiplication. Invertibility and Isomorphisms. The Change
of Coordinate Matrix. Dual Spaces. Homogeneous Linear Differential Equations
with Constant Coefficients.
3. Elementary Matrix Operations and Systems of Linear Equations. Notes3&4
Ø
Elementary Matrix Operations and Elementary
Matrices. The Rank of a Matrix and Matrix Inverses. Systems of Linear
Equations—Theoretical Aspects. Systems of Linear Equations—Computational
Aspects.
4. Determinants.
Ø
Determinants of Order 2. Determinants of Order n.
Properties of Determinants. Summary—Important Facts about Determinants. A
Characterization of the Determinant.
5. Diagonalization. Notes
Ø
Eigenvalues and Eigenvectors. Diagonalizability.
Matrix Limits and Markov Chains. Invariant Subspaces and the CayleyHamilton
Theorem.
6. Inner Product Spaces. Notes
Ø
Inner Products and Norms. The GramSchmidt
Orthogonalization Process and Orthogonal Complements. The Adjoint of a Linear
Operator.
7. Canonical Forms.
Ø
The
Calculation of Grade:
Homework  30%
Presentation  20%
Midterm exam  25% Study Guide
Final exam  25%
I will use the following scale for your grade in this course:
A: 92pts or above
A: 90pts or above
B+: 87pts or above
B: 82pts or above
B: 80pts or above
C+: 77pts or above
C: 72pts or above
C or lower is considered failing in a 500 level course
Exams
There will be a
Midterm Exam and an inclass Final. Your Midterm Exam will be on Thursday, Oct 25 and your final
will be Tuesday, Dec 18. The exams will test your
understanding of the material we cover in class. You will need to recall the theorems that we
covered and understand their significance, answer questions in general about
implications of these theorems. Before each test, I will provide you with a
list of theorems from class that I would expect you to be able to prove.
Homework Assignments:
Problem sets from the book will be assigned
throughout the semester. The book
includes some exercises for working out examples and some statements to
prove. You do not need to hand in
solutions to all the exercises assigned.
Only hand in the ones indicated.
For the others, check the answers in the back of the book. For the theory questions, which require a
proof, you are expected to write the solutions up carefully and hand them in by
the due dates given. This list will be updated as we go.
Assignments
Section 
Exercises 
Hand In 
Due Date 
1.2 
1, 12, 13, 14, 15 
 

1.3 
1, 6, 8, 11, 18, 20 
HK#1  6, 18, 20 
Sept 13 
1.4 
1, 2a, 2c, 5a, 5c, 10, 12 
HK#2  10,
12 
Sept 18 
1.5 
1, 2, 9, 16 
HK#3  16 
Sept 20 
1.6 
1, 2c, 2e, 9, 12, 29 
HK#4  12 
Sept 25 
2.1 
3, 6, 13, 14, 29 
HK #5  14, 29 
Sept 27 
2.2 
2b, 2e, 4, 8 
HK #6  4 
Oct 2 
2.3 
3, 9 
HK #7  9 
Oct 4 
2.4 
4, 5, 6, 9, 10 
HK #8  9, 10 
Oct 9 
2.5 
2a, 2c, 5, 9, 10 
HK #9  9,
10 
Oct 11 
2.6 
3 


3.1 
7 
HK #10  7 
Oct 23 
3.2 
19, 21, 22 
HK #11  22 
Oct 30 
4.2 
23, 28, 30 
HK #12  23, 28 
Oct 30 
5.1 

HK #13  6, 12 
Nov 1 
5.2 

HK #14  12 
Nov 6 
5.4 

HK # 15  11 
Nov 8 
6.1 

HK #16  10, 12 
Nov 20 
6.2 

HK #17 – 10 
Nov 27 
6.3 

“ – 13a 
Nov 27 
6.4 

HK #18 – 12 
Nov 29 
6.5 

HK #19 – 10, 12, 13 
Dec 4 
6.6 



7.1 

HK#20 classwork 
Dec 6 
HkPts: Each exercise
will be graded and comments will be given.
Each is worth up to 4 HkPts. The grade on your homework will be the
percent of points out of the total possible number of points – to be determined
(close to 150).
Here are some tips in doing homework.
Try each
problem on your own.
Check your
answer with someone from class.
Ask me about
the ones that you still do not completely understand.
Take notes
whenever we go over a problem in class.
Carefully
write a final version of each problem, as best you can, and keep them together
in a binder.
Presentation: Present one theorem to the
class from the following list. Also
solve the homework problem given. We
will follow the book order of the theorems in this course, and when we get to
yours, it will be your turn to present it.
Present it in chalk on the board, but provide a handout with all the
details given. Provide the solution to
the exercise as well in your handout. We
may or may not have time to go over your solution to the exercise in the
class. Keep in mind that during your
presentation, you must provide the proofs of all parts that are missing in the
book. For instance, the proof given in
the book may refer to an exercise. If
so, you should provide the proof of that exercise. Please refer to all theorems by their
statements rather than their number.
These are to be typed.
1. Theorem 1.6 and Corollary. Section 1.6, Number 29  M. Heissan
2. Theorem 4.7. Section
4.3, Number 15 – A. Gilbert
3. Theorem
5.22. Section 5.4, Number 7  N.
Vankayalapati
4. Corollary to
Theorem 5.23. Section 5.4, Number 5
– Q. Ding
5. Theorem 5.25. Section 5.4, Number 23 – J. Stockford
6. Theorem 6.1.
Section 6.2, Number 6 – D. Hadley
7. Theorem 6.2. Section
6.2, Number 11 – C. Lynd
8. Theorem 6.15. Section 6.4, Number 6 – M. Drymonis
Guide to
working with others:
There are
benefits to discussing the problems with your classmates. If you become
stuck on a problem, fresh ideas from someone else might provide you with some
new angles to try. In the academic community as well as in business and
industry, people often work in teams. So, it is good to get some practice
working with others. Working with someone from class will help you to
improve your math communication skills as well.
I encourage you to work together under the following circumstances.
Ø
Begin the problem on your own and
do as much as you can.
Ø
Ask someone from the class to
explain the basic outline of a solution.
Ø
If working with someone else, sometimes
they will also ask you for your understanding of the basic outline.
Ø
Take what you learned and write
out the solution on your own, using your own words.
Ø
Never copy word for word from
anyone else’s paper. In fact it is better not to look at anyone else’s
completed written solution or to show yours to anyone else.
Ø
If you still do not completely
understand the solution, you can ask your professor to look at what you wrote
and try to clear up any parts of the solution that are not completely clear and
accurate.
The following is an excerpt from
the University Manual.
8.27.11 A student's name on any written exercise
(theme, report, notebook, paper, examination) shall be regarded as assurance
that the work is the result of the student's own thought and study, stated in
the student's own words and produced without assistance, except as quotation
marks, references and footnotes acknowledge the use of other sources of
assistance. Occasionally, students may be authorized to work jointly, but such
effort must be indicated as joint on the work submitted. Submitting the
same paper for more than one course is considered a breach of academic
integrity unless prior approval is given by the instructors.
Schedule

Tuesday 

Thursday 

September 


6 
Chapter 1 

11 
Chapter 1 
13 
2.1, 2.2 

18 
2.3 
20 
2.4 

25 
2.5 
27 
2.6 
October 
2 
3.1 
4 
3.2 

9 
4.2 
11 
4.3 

16 
5.1 
18 
5.2 

23 
5.4 
25 
Midterm Exam 

30 
6.1 
1 
6.2 
November 
6 
6.3 
8 
6.4 

13 
6.5 
15 
6.6 

20 
6.7 
22 
6.10 

27 
7.1 
29 
7.1 
December 
4 
7.2 
6 
7.3 








20 – 3pm 
Final 