# Linear Algebra

### Linear Algebra Syllabus

• Course Code: Math 341

Transcript:

Yes. Your transcript will come from the records office at United States University. They are regionally accredited and award semester credits.

Credit: 4 Semester

Transfer: 4 year degree applicable

Enrollment Schedule:

Enroll any day of the year, and start that same day. Students have five months of access, plus a 30 day extension at the end if needed. Students can finish the self-paced courses as soon as they are able. Most students finish the lower level courses in 4 - 8 weeks. The upper level math classes, such as Calculus and above, usually take students 3-4 months. (Note: The 30-day extension cannot take your total course time six months beyond the date of enrollment. At the end of the six months, we must post a grade with the university.)

Required Textbook:

Yes, this course requires a textbook.

Proctored Final: Yes

#### Description

This course includes the study of vectors in the plane and space, systems of linear equations, matrices, determinants, vector spaces, linear transformations, inner products, eigenvalues, eigenvectors, diagonalization, matrix decomposition, and the Spectral Decomposition theorem.
Prerequisite: Calculus l with a grade of C or better. Methods of Proof is recommended.

#### Learning Outcomes

At the conclusion of this course, students should be able to:

1. Perform matrix operations and calculate determinants.
2. Understand the concept of matrices and their role in linear algebra and applied mathematics.
3. Understand linear systems Ax = b and the role of subspaces, linear independence, etc. in the analysis of these systems.
4. Understand eigenvalues, eigenvectors and their role in diagonalization.
5. Understand linear transformations and their properties over Rn.
6. Understand important definitions in Linear Algebra and the ability to write elementary proofs.

#### Methods of Evaluation:

Homework 15%
7 Chapter Tests 60%
Proctored Final Exam 25%
(You must get at least 60% on the proctored final in order to pass the class with a C or better.)

#### Homework Quizzes: 15%

Homework assignments are essential in a mathematics course. It is not possible to master the course without a considerable amount of time being devoted to studying the concepts and solving problems. Each lesson contains a set of homework problems, and you are required to do all the problems for each section. Work out each problem, and then check the answer. Do not continue to the next problem until you understand your mistake. It is important to figure what you did wrong before you push forward. If you figure out your errors at this step, you will be less likely to make the same error on the chapter test and/or the final exam. The struggle to figure out what you did wrong stores the mathematics into your long-term memory, and aids in building abstract thinking.

#### Chapter Tests: 60%

After you have completed a chapter, and understand everything in the lessons and the homework, take the practice quiz. Then when you are ready, take chapter test. The chapter tests are revised problems from the homework. Again, once you take a chapter test, figure out what you did wrong before moving forward.

#### Proctored Final: 25%

This course go towards a degree which means it must have a proctored final. Your college is accepting this course because it goes through a regionally accredited university, which tells them the class will have a proctored final, and the 60% rule will apply. Your college will not accept a class from a school that is not regionally accredited, because they know these standards won't be met.

The final exam must be proctored at college testing center or a Sylvan Learning Center. A valid driver's license or State ID must be shown at the testing center. An expired license or State ID will not be accepted. Use this link to help you find a college testing center or Sylvan Learning center near your home: Proctored Final

The final exam is a comprehensive final covering all of the chapters of the course. Other than scratch paper, you may view the "Authorized Materials" list for the final exam for each class.

• Students must obtain a 60% or better on the final exam in order to get a C or better in the class.
• Students that obtain a grade of an F on the final can receive at most a D in the class. Students that obtain a D on the final can receive at most a C in the class. Students that obtain a C on the final can receive at most a B in the class.

The 60% rule was set in place to protect the integrity of online math education by requiring a display of competency in exchange for a grade. All schools which are regionally accredited adhere to online standards. Your college is accepting this course because it goes through a regionally accredited university, which tells your college that standards have been met. Your college will not accept a class from a school that is not regionally accredited, because they know the standards won't be met.

#### Assessment:

A 90-100 A Clearly stands out as excellent performance and, exhibits mastery of learning outcomes.
B 80-89 B Grasps subject matter at a level considered to be good to very good, and exhibits partial mastery of learning outcomes.
C 70-79 C Demonstrates a satisfactory comprehension of the subject matter, and exhibits sufficient understanding and skills to progress in continued sequential learning.
D 60-69 D Quality and quantity of work is below average and exhibits only partial understanding and skills to progress in continued sequential learning.
F 0-59 F Quality and quantity of work is below average and not sufficient to progress.

## Chapter 1

Linear Equations in Linear Algebra

Lessons Homework
1.1 Systems of Linear Equations 1.1
1.2 Row Reduction and Echelon Forms 1.2
1.3 Vector Equations 1.3
1.4 The Matrix Equation Ax = b 1.4
1.5 Solution Sets of Linear Systems 1.5
1.6 Applications of Linear Systems 1.6
1.7 Linear Independence 1.7
1.8 Introduction to Linear Transformations 1.8
1.9 The Matrix of a Linear Transformation 1.9
Exam Chapter 1

## Chapter 2

Matrix Algebra

Lessons Homework
2.1 Matrix Operations 2.1
2.2 The Inverse of a Matrix 2.2
2.3 Characterizations of Invertible Matrices 2.3
2.4 Partitioned Matrices 2.4
2.5 Matrix Factorizations 2.5
2.8 Subspaces of Rn 2.8
2.9 Dimension and Rank 2.9
Exam Chapter 2

## Chapter 3

Determinants

Lessons Homework
3.1 Introduction to Determinants 3.1
3.2 Properties of Determinants 3.2
3.3 Cramer's Rule, Volume and Linear Transformations 3.3
Exam Chapter 3

## Chapter 4

Vector Spaces

Lessons Homework
4.1 Vector Spaces and Subspaces 4.1
4.2 Null Spaces, Column Spaces, and Linear Transformations 4.2
4.3 Linearly Independent Sets; Bases 4.3
4.4 Coordinate System 4.4
4.5 The Dimension of a Vector Space 4.5
4.6 Rank 4.6
4.7 Change of Basis 4.7
Exam Chapter 4

## Chapter 5

Eigenvalues and Eigenvectors

Lessons Homework
5.1 Eigenvalues and Eigenvectors 5.1
5.2 The Characteristic Equation 5.2
5.3 Diagonalization 5.3
5.4 Eigenvectors and Linear Transformations 5.4
5.5 Complex Eigenvalues 5.5
Exam Chapter 5

## Chapter 6

Orthogonality and Least Squares

Lessons Homework
6.1 Inner Product, Length, and Orthogonality 6.1
6.2 Orthogonal Sets 6.2
6.3 Orthogonal Projections 6.3
6.4 The Gram-Schmidt Process 6.4
6.5 Least-Squares Problems 6.5
6.6 Applications to Linear Models 6.6
6.7 Inner Product Spaces 6.7
Exam Chapter 6

## Chapter 7

Symmetric Matrices and Quadratic Forms

Lessons Homework
7.1 Diagonalization of Symmetric Matrices 7.1
7.2 Quadratic Forms 7.2
7.3 Constrained Optimization 7.3
7.4 The Singular Value Decomposition 7.4
Exam Chapter 7
Final Exam

#### Time on Task:

This course is online and your participation at home is imperative. A minimum of 8 - 10 hours per week of study time is required for covering all of the online material to achieve a passing grade. You must set up a regular study schedule. You have five months of access to your online account with a thirty-day extension at the end if needed. If you do not complete the course within this time line, you will need to enroll in a second term.

#### Schedule:

Below is the suggested time table to follow to stay on a 17 week schedule for the course. The following schedule is the minimum number of sections that need to be completed each week if you would like to finish in a regular semester time frame. You do not have to adhere to this schedule. You have five months of access plus a 30 day extension at the end if needed. You can finish the course as soon as you are able.

 Week Complete Sections 1 1.1 - 1.3 2 1.4 - 1.6 3 1.7 - 1.9 4 2.1 - 2.3 5 2.4 - 2.6 6 2.7 - 2.9 7 3.1 - 3.3 8 4.1 - 4.3 9 4.4 - 4.6 10 4.7 - 5.2 11 5.3 - 5.5 12 6.1 - 6.2 13 6.3 - 6.4 14 6.5 - 6.6 15 6.7 - 7.1 16 7.2 - 7.4 Final Exam

## Conduct Code:

#### Code of Ethics:

Regulations and rules are necessary to implement for classroom as well as online course behavior. Students are expected to practice honesty, integrity and respect at all times. It is the student's responsibility and duty to become acquainted with all provisions of the code below and what constitutes misconduct. Cheating is forbidden of any form will result in an F in the class.

#### Respectful communications:

When contacting Omega Math or Westcott Courses, you agree to be considerate and respectful. Communications from a student which are considered by our staff to be rude, insulting, disrespectful, harassing, or bullying via telephone, email, or otherwise will be considered a disrespectful communication and will result in a formal warning.

We reserve the right to refuse service. If we receive multiple disrespectful communications from person(s) representing the student, or the student themselves, the student will be excluded from taking future courses at Westcott Courses/Omega Math.

#### Examples of academic misconduct:

Cheating: Any form of cheating will result in an F in the class. If there is an associated college attached to the course, that college will be notified of the F due to cheating and they will determine any disciplinary action.

Any form of collaboration or use of unauthorized materials during a quiz or an exam is forbidden.

By signing up for a course, you are legally signing a contract that states that the person who is named taking this course is the actual individual doing the course work and all examinations. You also agree that for courses that require proctored testing, that your final will be taken at a college testing center, a Sylvan Learning center, and the individual signed up for this course will be the one taking the test. Failure to do so will be considered a breach of contract.

Other forms of cheating include receiving or providing un-permitted assistance on an exam or quiz; taking an exam for another student; using unauthorized materials during an exam; altering an exam and submitting it for re-grading; failing to stop working on the exam when the time is up; providing false excuses to postpone due dates; fabricating data or references, claiming that Westcott Courses/Omega Math lost your test and or quiz scores. This includes hiring someone to take the tests and quizzes for you.

#### Unauthorized collaboration:

Working with others on graded course work without specific permission of the instructor, including homework assignments, programs, quizzes and tests, is considered a form of cheating.

#### Important Notes:

This syllabus is subject to change and / or revision during the academic year. Students with documented learning disabilities should notify our office upon enrollment, as well as make sure we let the testing center know extended time is permitted. Valid documentation involves educational testing and a diagnosis from a college, licensed clinical psychologist or psychiatrist.

• Course Code: None

Transcript:

A certificate of completion is issued from Omega Math. This course under the non-credit option does not go through one of our partner universities; thus, a transcript is not included with the course.

Credit: 0

Certificate of Completion: Yes

Transfer:

If you would like to take this class for personal enrichment, the non-credit course is the exact same class as the credit course; it is just less expensive since it is not sent through our partner university for credit. If you want to transfer the course to your college, you will need to enroll under the semester credit option. If you would like pre-approval from your school, please send your counselor or registrar's office the link to this page. The non-credit courses can also be used to learn the material and then receive credit at a home college using Credit by Examination. (K-12 use)

Enrollment Schedule:

Enroll any day of the year, and start that same day. Students have five months of access, plus a 30 day extension at the end if needed. Students can finish the self-paced courses as soon as they are able. Most students finish the lower level courses in 4 - 8 weeks. The upper level math classes, such as Calculus and above, usually take students 3-4 months. (Note: The 30-day extension cannot take your total course time six months beyond the date of enrollment. At the end of the six months, we must post a grade with the university.)

Required Textbook:

Yes, this course requires a textbook.

Proctored Final: No

#### Description

This course includes the study of vectors in the plane and space, systems of linear equations, matrices, determinants, vector spaces, linear transformations, inner products, eigenvalues, eigenvectors, diagonalization, matrix decomposition, and the Spectral Decomposition theorem.
Prerequisite: Calculus l with a grade of C or better. Methods of Proof is recommended.

#### Learning Outcomes

At the conclusion of this course, students should be able to:

1. Perform matrix operations and calculate determinants.
2. Understand the concept of matrices and their role in linear algebra and applied mathematics.
3. Understand linear systems Ax = b and the role of subspaces, linear independence, etc. in the analysis of these systems.
4. Understand eigenvalues, eigenvectors and their role in diagonalization.
5. Understand linear transformations and their properties over Rn.
6. Understand important definitions in Linear Algebra and the ability to do very elementary proofs.

#### Methods of Evaluation:

Quizzes 35%
Midterm 20%
Homework 20%
Proctored Final Exam 25%
(You must get at least 60% on this final in order to pass the class with a C or better.)

#### Homework Quizzes: 15%

Homework assignments are essential in a mathematics course. It is not possible to master the course without a considerable amount of time being devoted to studying the concepts and solving problems. Each lesson contains a set of homework problems, and you are required to do all the odd problems for each section. Work out each problem, and then check the solution manual for a detailed solution. Do not continue to the next problem until you understand your mistake. Once you feel comfortable with the homework set, take the homework quiz for that section. The homework quizzes are revised problems from the homework sets. You may take each quiz twice, and the higher of the two scores is used to calculate your quiz grade. Once you take a quiz, figure out what you did wrong on the problems that you missed and then try the quiz again. It is important to figure what you did wrong before you push forward. If you figure out your errors at this step, you will be less likely to make the same error on the test or the final. The struggle to figure out what you did wrong stores the mathematics into your long-term memory, and aids in building abstract thinking.

#### Chapter Tests: 60%

After you have completed a chapter, and understand everything in the lessons, homework sets and quizzes, take the chapter test. The chapter tests are revised problems from the quizzes. You may take each chapter test twice, and the higher of the two scores is used to calculate your chapter test grade. Once you take a chapter test, figure out what you did wrong on the problems that you missed and then try the chapter test again. It is important to figure what you did wrong before you push forward. If you figure out your errors at this step, you will be less likely to make the same error on the final.

#### Assessment:

A 90-100 A Clearly stands out as excellent performance and, exhibits mastery of learning outcomes.
B 80-89 B Grasps subject matter at a level considered to be good to very good, and exhibits partial mastery of learning outcomes.
C 70-79 C Demonstrates a satisfactory comprehension of the subject matter, and exhibits sufficient understanding and skills to progress in continued sequential learning.
D 60-69 D Quality and quantity of work is below average and exhibits only partial understanding and skills to progress in continued sequential learning.
F 0-59 F Quality and quantity of work is below average and not sufficient to progress.

## Chapter 1

Linear Equations in Linear Algebra

Lessons Homework
1.1 Systems of Linear Equations 1.1
1.2 Row Reduction and Echelon Forms 1.2
1.3 Vector Equations 1.3
1.4 The Matrix Equation Ax = b 1.4
1.5 Solution Sets of Linear Systems 1.5
1.6 Applications of Linear Systems 1.6
1.7 Linear Independence 1.7
1.8 Introduction to Linear Transformations 1.8
1.9 The Matrix of a Linear Transformation 1.9

## Chapter 2

Matrix Algebra

Lessons Homework
2.1 Matrix Operations 2.1
2.2 The Inverse of a Matrix 2.2
2.3 Characterizations of Invertible Matrices 2.3
2.4 Partitioned Matrices 2.4
2.5 Matrix Factorizations 2.5
2.8 Subspaces of Rn 2.8
2.9 Dimension and Rank 2.9

## Chapter 3

Determinants

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

## Chapter 4

Vector Spaces

Lessons Homework
4.1 Vector Spaces and Subspaces 4.1
4.2 Null Spaces, Column Spaces, and Linear Transformations 4.2
4.3 Linearly Independent Sets; Bases 4.3
4.4 Coordinate System 4.4
4.5 The Dimension of a Vector Space 4.5
4.6 Rank 4.6
4.7 Change of Basis 4.7

## Chapter 5

Eigenvalues and Eigenvectors

Lessons Homework
5.1 Eigenvalues and Eigenvectors 5.1
5.2 The Characteristic Equation 5.2
5.3 Diagonalization 5.3
5.4 Eigenvectors and Linear Transformations 5.4
5.5 Complex Eigenvalues 5.5

## Chapter 6

Orthogonality and Least Squares

Lessons Homework
6.1 Inner Product, Length, and Orthogonality 6.1
6.2 Orthogonal Sets 6.2
6.3 Orthogonal Projections 6.3
6.4 The Gram-Schmidt Process 6.4
6.5 Least-Squares Problems 6.5
6.6 Applications to Linear Models 6.6
6.7 Inner Product Spaces 6.7

## Chapter 7

Symmetric Matrices and Quadratic Forms

Lessons Homework
7.1 Diagonalization of Symmetric Matrices 7.1
7.2 Quadratic Forms 7.2
7.3 Constrained Optimization 7.3
7.4 The Singular Value Decomposition 7.4

#### Time on Task:

This course is online and your participation at home is imperative. A minimum of 8 - 10 hours per week of study time is required for covering all of the online material to achieve a passing grade. You must set up a regular study schedule. You have five months of access to your online account with a thirty-day extension at the end if needed. If you do not complete the course within this time line, you will need to enroll in a second term.

#### Schedule:

Below is the suggested time table to follow to stay on a 17 week schedule for the course. The following schedule is the minimum number of sections that need to be completed each week if you would like to finish in a regular semester time frame. You do not have to adhere to this schedule. You have five months of access plus a 30 day extension at the end if needed. You can finish the course as soon as you are able.

 Week Complete Sections 1 1.1 - 1.3 2 1.4 - 1.6 3 1.7 - 1.9 4 2.1 - 2.3 5 2.4 - 2.6 6 2.7 - 2.9 7 3.1 - 3.3 8 4.1 - 4.3 9 4.4 - 4.6 10 4.7 - 5.2 11 5.3 - 5.5 12 6.1 - 6.2 13 6.3 - 6.4 14 6.5 - 6.6 15 6.7 - 7.1 16 7.2 - 7.4 Final Exam

## Conduct Code:

#### Code of Ethics:

Regulations and rules are necessary to implement for classroom as well as online course behavior. Students are expected to practice honesty, integrity and respect at all times. It is the student's responsibility and duty to become acquainted with all provisions of the code below and what constitutes misconduct. Cheating is forbidden of any form will result in an F in the class.

#### Respectful communications:

When contacting Omega Math or Westcott Courses, you agree to be considerate and respectful. Communications from a student which are considered by our staff to be rude, insulting, disrespectful, harassing, or bullying via telephone, email, or otherwise will be considered a disrespectful communication and will result in a formal warning.

We reserve the right to refuse service. If we receive multiple disrespectful communications from person(s) representing the student, or the student themselves, the student will be excluded from taking future courses at Westcott Courses/Omega Math.

#### Examples of academic misconduct:

Cheating: Any form of cheating will result in an F in the class. If there is an associated college attached to the course, that college will be notified of the F due to cheating and they will determine any disciplinary action.

Any form of collaboration or use of unauthorized materials during a quiz or an exam is forbidden.

By signing up for a course, you are legally signing a contract that states that the person who is named taking this course is the actual individual doing the course work and all examinations. You also agree that for courses that require proctored testing, that your final will be taken at a college testing center, a Sylvan Learning center, and the individual signed up for this course will be the one taking the test. Failure to do so will be considered a breach of contract.

Other forms of cheating include receiving or providing un-permitted assistance on an exam or quiz; taking an exam for another student; using unauthorized materials during an exam; altering an exam and submitting it for re-grading; failing to stop working on the exam when the time is up; providing false excuses to postpone due dates; fabricating data or references, claiming that Westcott Courses/Omega Math lost your test and or quiz scores. This includes hiring someone to take the tests and quizzes for you.

#### Unauthorized collaboration:

Working with others on graded course work without specific permission of the instructor, including homework assignments, programs, quizzes and tests, is considered a form of cheating.

#### Important Notes:

This syllabus is subject to change and / or revision during the academic year. Students with documented learning disabilities should notify our office upon enrollment, as well as make sure we let the testing center know extended time is permitted. Valid documentation involves educational testing and a diagnosis from a college, licensed clinical psychologist or psychiatrist.