# MA 322 003 Matrix Algebra and its Applications

Instructor: Rafael S. González D'León
Email: rafaeldleon@uky.edu
Homepage: http://www.ms.uky.edu/~rsgo226
Office: Patterson Office Tower, Room 767.
Office Hours: TW 2:00PM to 3:00PM or by appointment.

## Lectures

Monday, Wednesday and Fridays 11:00AM-12:00PM CB 347.

## Literature

Linear Algebra and its applications. David C. Lay. Fourth edition.

## Course Contents

The solution of simultaneous linear equations. Matrix algebra. Determinants. Vector spaces. Eigenvalues and Eigenvectors. Inner product spaces and least squares approximation. Most of chapters 1 to 6 from Lay's book.

## Examination and Grading

### Tests (50%)

There will be 2 tests. These will be announced at least one week in advance.

### Final (30%)

There will be a comprehensive final to be worth 30% on Monday 5/2/2016 10:30-12:30 A.M..

### Homework and Quizzes (20%)

There will be online homework to be handed in every week.
The online homework will be assigned and completed in Webwork (http://webwork.as.uky.edu/webwork2/MA322003S16). Your username is your LinkBlue ID (use only capital letters), and your password is your student ID number (8 digits).

There may also be some additional written homework. These problems will be assigned after some of the classes and also posted in the web page of the course.
There will be some (unannounced) quizzes on some Wednesdays.
Homework and quizzes are equally weighted for the remaining 20% of the grade.

>=90%A
>=80%B
>=70%C
>=60%D
<60%E

### Suggested exercises

There is a list of suggested exercises that you can find in http://dleon.combinatoria.co/pages/courses/suggestedproblemsma322003-201601.html. You are expected to complete at least one third of the problems in this list. Some of these problems could appear in the quizzes, tests and the final exam.

## Syllabus

This is an approximate schedule of the course containing the syllabus:
DateTopic
Wed 1/13Introduction. 1.1 Systems of Linear Equations
Fri 1/151.2 Row Reduction and Echelon Forms
Wed 1/201.3 Vector Equations
Fri 1/221.4 The Matrix Equation Ax = b
Mon 1/251.5 Solution Sets of Linear Systems
Wed 1/271.7 Linear Independence
Fri 1/291.8 Introduction to Linear Transformations
Mon 2/11.9 The Matrix of a Linear Transformation
Wed 2/32.1 Matrix Operations
Fri 2/52.2 The Inverse of a Matrix
Mon 2/82.3 Characterizations of Invertible Matrices
Wed 2/102.5 Matrix Factorizations
Fri 2/123.1 Introduction to Determinants
Mon 2/15Review Test 1
Wed 2/17TEST 1
Fri 2/193.2 Properties of Determinants
Mon 2/223.3 Cramer’s Rule, Volume, and Linear Transformations
Wed 2/244.1 Vector Spaces and Subspaces
Fri 2/264.1 Vector Spaces and Subspaces
Mon 2/294.2 Null Spaces, Column Spaces, and Linear Transformations
Wed 3/24.2 Null Spaces, Column Spaces, and Linear Transformations
Fri 3/44.3 Linearly Independent Sets; Bases
Mon 3/74.4 Coordinate Systems
Wed 3/94.5 The Dimension of a Vector Space
Fri 3/114.6 Rank
Mon 3/214.7 Change of Basis
Wed 3/234.9 Applications to Markov Chains
Fri 3/255.1 Eigenvectors and Eigenvalues
Mon 3/285.2 The Characteristic Equation
Wed 3/30Review Test 2
Fri 4/1TEST 2
Mon 4/45.3 Diagonalization
Wed 4/65.4 Eigenvectors and Linear Transformations
Fri 4/85.4 Eigenvectors and Linear Transformations
Mon 4/11More applications of Eigenvalues and Eigenvectors
Wed 4/136.1 Inner Product, Length, and Orthogonality
Fri 4/156.1 Inner Product, Length, and Orthogonality
Mon 4/186.2 Orthogonal Sets
Wed 4/206.3 Orthogonal Projections
Fri 4/226.4 The Gram—Schmidt Process
Mon 4/256.5 Least-Squares Problems
Wed 4/276.8 Applications of Inner Product Spaces
Fri 4/29Review Final
Mon 5/2FINAL EXAM 10:30-12:30 A.M.

The university and the department of mathematics offer tutoring without appointment at The Mathskeller . The Study also offers peer tutoring.

## Calculators Policy

Calculators are not allowed in quizzes, tests or the final exam.

## Code of Conduct

Students should consult the students rights and responsibilities outlined in the Student Code of Conduct. Any offense to the Code of Conduct will result in a grade of "E" for the course and a referral to the Dean of Students.

## Excused Absences

University Senate Rule 5.2.4.2 defines the following acceptable reasons for an ”excused absence” from class:
• Serious illness (must be documented by doctor’s excuse)
• Illness or death of a family member
• University-related trips (must be documented by a letter from sponsor)
• Major religious holidays
• Other circumstances that your instructor finds to be ”reasonable cause for nonattendence”
Students should notify the instructor of an excused absence prior to the absence whenever possible and complete all work prior to the absence (unless for illness or for the illness or death of a family member).

## Students with Disabilities

Students with documented physical‚ learning‚ or temporary disabilities may receive assistance and support from the Disability Resource Center. It is recommended that students contact the Disability Resource Center early to request specific assistance so that the required medical or psychological documentation can be reviewed and reasonable accommodations can be provided from the beginning of class work in order to achieve the greatest benefit to the student.

## Changes to this Syllabus

This syllabus can have some changes during the semester. It is responsibility of the students to visit frequently the webpage of the course for up to date information.