Math 225, Section R2, Fall 2007

Homework assignments Approximate Schedule, Score Reports, Syllabus

Problems from Exam2 of previous semester Answer

Lectures: TR 1:00-1:50pm in 142 Henry BLD
Instructor: Tao Mei, mei@math.uiuc.edu
Course homepage: www.math.uiuc.edu/~mei/math225.html
Office & Telephone: ALTGELD Hall 109, 217-244-2478
Office Hours: 9:30-10:50am Tuesday or by appointment.
Textbook (required): David C. Lay, Linear Algebra and its Applications, 3^rd Edition, Addison-Wesley, 2006.

Course Description: This course will cover the most contents of Chapters 1, 2, 3, 4 and 5 of the textbook. Students should understand and master the basic theory in Matrix Theory and its applications. See the Approximate Schedule for information of which section will be covered.

Tentative exam dates: There will be three hour-long exams during the semester and a final exam. Books, notes, calculators are not allowed on exams.

Exam #1 – 7:00-8:00pm, Tuesday, Sept. 18^th, 241 Altgeld.

The exam covers section 1.1-1.5,1.7, 2.1-2.3.

We will have a review session in our regular class Sept. 18^th.

Extra office hours: 5-6pm Sept. 18^th.

Conflict exam: 11:00-12:00am Sept. 19th, meet me by 10:50 am Wednesday with a proof of your conflict time.

The exam problems for chapter 2 will be like the quiz problems. For chapter 1, you need to know how to solve systems and related problems such as, linear dependent, Span of a set of vectors, reduced echelon forms, solutions of a system in parametric vector form…, Understanding Theorem 8 on page 129 of the textbook is very helpful for understanding all material in Chapter 1 and 2.

Exam #2 - 7:00-8:00pm, Tuesday, Oct. 16^th, 241 Altgeld.

The exam will cover section 3.1-3.3, 4.1,4.2.

We will have a review session in our regular class on Oct. 16^th. Extra office hours: 5-6pm Monday, Oct. 15th.

Conflict exam: 7-8pm Oct. 17^th, 241 Altgeld.

Exam #3 – 7:00-8:00pm, Tuesday, Nov. 13^th, 241 Altgeld.

Exam 3 will cover section 4.2, 4.3, 4.5,4.4 and Theorem 10 of section 3.3.

We will have a review session in our regular class on Nov. 13^th. Extra office hours: 5-6pm Monday, Nov. 12th.

Conflict exam: 7-8pm Nov. 14^th, 241 Altgeld.

Suggested practice problems: Section 4.2: #2, 11, 21, 24, 25, 26, 30, Section 3.3: #27, 28, Section 4.3: #10,14,16,20, 21, 22, 23, 25, 34, Section 4.5: #4, 6, 8,12, 14, Section 4.6: #4, 6, 11, 18, 19, 25, 27, 28;

Final Exam- 1:30–4:30 PM, Wednesday, December 12 in our regular classroom (142 Henry building). Please arrange any travel, etc., so that you can take the final on this date. Math 225 has a "non-combined" final exam. There will be no conflict exam given except for those few individuals who meet the official university criteria given here in the student code.

Contents covered: Section 1.1-1.5, 1.7, 2.1-2.3, 3.1-3.3, 4.1-4.3,4.5-4.6,5.1-5.2(except “similarity”).

You need a really strong reason to take the conflict exam. Meet me in my office 1:50pm on Friday, Dec. 7^th unless you have other agreement with me.

Missed exams: If you miss an exam, you will receive a 0 for your grade. The only exception is if you have a valid excuse for missing, such as academic conference, major illness or a serious emergency - if so, you must inform me before the exam, preferably by email. And you need a note from your academic advisor or your doctor. Notify me no later than one day after the test to set up a time for a make up.

Homework: We will have a homework assignment each week. Written homework is due at the beginning of class on the due date. The two poorest scores of your home work will be dropped out.

Homework Rules: (1)Print your name, section at the top of the paper. (2) Staple the papers together if your homework takes more than one page. (3) Work out the problems, the answer only will not be accepted.(5)Be neat and legible.

You will be able to check your homework and exam grades at Score Reports, which is the Math Department's gradebook program. This will be available beginning approximately two weeks into the semester. All your h/work, quiz and exam grades will be posted there. You will be prompted for your NetID and NetID password after following the Score Reports link. Please check score reports regularly to make sure your grades have been correctly reported and tell me promptly about any errors. You are responsible for keeping all of your graded homework and exams so that any discrepancies in recorded grades can be settled.

Approximate Course Schedule

(Each section will be covered in about one class hour.)

Chapter 1: Linear Equations in Linear Algebra

1.1 Systems of Linear Equations
1.2 Row Reduction and Echelon Forms
1.3 Vector Equations
1.4 The Matrix Equation Ax=b
1.5 Solution Sets of Linear Systems
1.7 Linear Independence

Chapter 2:

2.1 Matrix Operations
2.2 The Inverse of a Matrix
2.3 Characterizations of Invertible Matrices
2.6 The Leontief Input-Output Model

Chapter 3: Determinants

3.1 Introduction to Determinants
3.2 Properties of Determinants
3.3 Cramer's Rule, Volume, and Linear Transformations

Chapter 4: Vector Spaces

4.1 Vector Spaces and Subspaces
4.2 Null spaces, Column Spaces, and Linear Transformations
4.3 Linearly Independent Sets: Bases
4.5 The Dimension of a Vector Space
4.6 Rank

Chapter 5: Eigenvalues and Eigenvectors

5.1 Eigenvalues and Eigenvectors
5.2 The Characteristic Equation
5.3 Diagonalization

Chapter 6: Orthogonality and Least Squares

6.1 Inner Product, Length, and Orthogonality
6.2 Orthogonal Sets
6.3 Orthogonal Projections
6.5 Least Squares Problems
6.6 Applications to Linear Models

Notes:
1. An hour exam will be given at the conclusion of Chapters 2, 3, and 4.

Homework Assignments (An complete assignment ends with a “.”. An assignment end with a “;” is incomplete, additional problems will be added to it later.)

Assignment #1 (due by the beginning of the class on Aug. 30^th, Thursday ) Exercise of section 1.1 of the textbook: #11 (solve it by using the augmented matrix); Section 1.2: #2, 7,21,30.
Assignment #2 (due by the beginning of the class on Sep. 6^th, Thursday ) Section 1.3: #11,21,22,25; Section 1.4: #3, 7,9,12,15,32; Section 1.5:#1,5,13,29,30; Section 1.7:#11,20,23,28,30.
Assignment #3 (due by the beginning of the class on Sep. 13^th, Thursday ) Section 2.1: #1,2, 4,5, 11,12; More of Section 2.1: #18,20,22,26; Section 2.2: 3,6,7,9,21,22.
Assignment#4 (due by the beginning of the class on Sep. 18^th, Tuesday ) More of section 2.2: #16,28,31, section 2.3:#13,15,17,21;
Assignment#5 (due by the beginning of the class on Oct. 2nd, Tuesday ) Section 3.1: #4,10,13,17,33; section 3.2; #7,18,19,21,31. Read the proof of Theorem 3,6 on Page 197. (A quiz of section 3.1-3.2 will be given in the class of Tuesday Oct. 2^nd).
Assignment#6 (due by the beginning of the class on Oct. 9th, Tuesday ) Section 3.3: #5 ,8,13,18; More on Section 3.3: #22,24, Page212: #9,13.
Assignment#7 (due by the beginning of the class on Oct. 16th, Tuesday ) Section 4.1: #5 ,6,10,15-18, 23,24; Section 4.2: #1,11.
Assignment#8 (due by the beginning of the class on Oct. 30th, Tuesday ) Section 4.2: #2,3,17,24,25;21,35, Section 3.3: #27, Read Table on page 232. (Please note “section 3.3” is what I mean, not a “typo”, we learned Theorem10 on page 207 thursday.)
Assignment#9 (due by the beginning of the class on Nov. 6th, Tuesday ) Section 4.3: #10,14,16,20,23; 21,25, Section 4.5: #4,8,12.
Assignment#10 (due by the beginning of the class on Nov. 13th, Tuesday ) Section 4.5: #12,14, 18, Section 4.6: #4,6,11,18,28;
Assignment#11 (due by the beginning of the class on Dec. 4th, Tuesday ) Section 5.1: #2,6, 8, 11,12,18, 23, 25; Section 5.2: #8,16. (please note one more problem of section 5.1 was added)