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MATH 2010 Syllabus

Course Syllabus

MATH 2010 - Introduction to Linear Algebra

3 Credit Hours

Course Information

Course Description:

This is the first course in matrix theory. Students will learn about basic matrix operations and definitions. The course will be problem-oriented with homework, quizzes and tests measuring understanding of vocabulary as well as applications.

Course Outcomes:

Upon successful completion of this course, students will be able to:

  • Use matrices to simplify and solve problems.
  • Represent a system of linear equations as a matrix.
  • Perform row operations on a matrix representing a system of linear equations in order to put the matrix in row reduced echelon form and read the solution set.
  • Determine if a system of equations is consistent and whether it has a unique solution
  • Solve systems of linear equations using Gauss-Jordan elimination.
  • Write a given matrix in row reduced echelon form.
  • Compute sums and products of matrices.
  • Convert between vector equations and systems of equations.
  • Compute the product of a matrix and a vector.
  • Determine if a vector is a linear combination of a set of vectors.
  • Solve a matrix equation of the form Ax=b.
  • Set up and solve word problems using matrices including economics, traffic flow
  • Balance chemical equations using matrices
  • analyze electrical networks
  • Solve a homogeneous linear system using one of the variables as a parameter.
  • Determine when sets of vectors are linearly independent
  • Find values to complete vectors to make them independent or dependent
  • Determine if columns of a matrix are linearly independent
  • Find the image of a vector under a linear transformation
  • Given a linear transformation T(x) = A x find x for a given vector b in the range.
  • Recognize reflections, retractions, and shears
  • Find the matrix of a linear transformation
  • Add, multiply and transpose matrices
  • Determine whether a given matrix is invertible and compute its inverse if it exists
  • State and apply properties of matrix algebra
  • perform matrix-vector multiplication and understand how this operation defines a linear transformation between Rn and Rm.
  • Solve Leontif applications with a simple economy
  • Compute determinants using cofactor expansion
  • Demonstrate the understanding of properties of determinants
  • Calculate determinant using row reduction
  • Use determinant to tell if a matrix is invertible
  • Use Cramer's Rule to solve a linear system
  • Find the area of parallelogram or parallelepiped using determinants
  • Explain the axiomatic definition of a vector space and know some examples of vector spaces other than Rn
  • Recognize which sets of vectors of Rn form a subspace
  • Find the vector spaces NulA and ColA for a given matrix
  • Recognize if a given function between vector spaces is a linear transformation
  • Explain the notions of the kernel and the image of a linear transformation and their relationship to the null space and the column space of a matrix
  • Find the dimension of the Null and Column spaces of a given matrix
  • Compute bases of some simple vector spaces 
  • Determine if a given set is a basis of R3
  • Find a basis for NulA and ColA for a given matrix A
  • Find a basis for a subspace of real-valued functions
  • Map a coordinate vector in a basis B to a vector in the standard basis
  • Compute coordinates of a vector space relative to a basis
  • Find the change of coordinates matrix from a basis B to the standard basis
  • Compute the dimension of a vector space in some simple examples
  • Compute dimensions of various subspaces defined by a matrix using the rank theorem
Prerequisites & Co-requisites:

MATH 1910 and MATH 1920

Course Topics:
  • Systems of linear equations
  • Matrices
  • Matrix algebra
  • Elementary row operations
  • Column operations
  • Determinants
  • Vector spaces and subspaces
  • Linear transformations between vector spaces
  • Linear independence between vectors
  • Matrix Inverses
  • Coordinate systems
Specific Course Requirements:

Students should have a basic knowledge of using a graphing calculator like the TI-83.

Textbooks, Supplementary Materials, Hardware and Software Requirements

Required Textbooks:

Please visit the Virtual Bookstore to obtain textbook information for this course. Move your cursor over the "Books" link in the navigation bar and select "Textbooks & Course Materials." Select your Program, Term, Department, and Course; then select "Submit."

Supplementary Materials:

A graphical calculator, such as TI-83.

Hardware and Software Requirements:

Minimum hardware requirements can be found here.

Minimum software requirements can be found here.

Common applications you might need:

Web Resources:

Purdue OWL Online Writing Lab (for APA, MLA, or Chicago style)

The Writing Center Online Writer's Handbook

Student Resources:
  • Technical support information can be found on the TN eCampus Help Desk page.
  • Smarthinking virtual tutoring is available FREE of charge. to access Smarthinking, visit the course homepage and select Smarthinking under Course Resources. You also view sample sessions to see what Smarthinking offers and how it works.
  • Information on other student issues or concerns can be located on the TN eCampus Student Resources page.

Instructor Information

Please see "Instructor Information" in the Getting Started Module for instructor contact information, virtual office hours, and other communication information. You can expect to receive a response from the instructor within 24-48 hours unless notified of extenuating circumstances.

Participation, Assessments, & Grading

Testing Procedures:


Grading Procedures:

Letter grades for this course will be assigned based on the following scale.

Percentage RangeAssigned Grade
90 - 100%A
80 - 89%B
70 - 79%C
60 - 69%D
under 60%F

Graded Items

DescriptionPercentage of Overall
8 Homework Assignments @ 3.13% each25%
12 Practice Quizzes @ 2.08% each25%
Mid-term Exam25%
Final Exam25%
Total Points100%
Grading Scale:
Assignments and Projects:

There are 8 Modules for this course.  Each Module consists of readings from the textbook or eTextbook, one homework assignment in MyLab Math (MML), leading up to one or two practice quizzes.  Email your instructor with any questions on the homework assignments.  There are instructor hints on the homework problems as well as "show me an example"  student aids.  Some Modules are longer than others and take two weeks.  For example, Module 1 takes two weeks, whereas Module 2 takes only one week.  Pay attention to the deadlines on MyMathLab homepage.  Modules 1 - 4 will precede the Midterm Exam.  Modules 5 - 8 will culminate with the comprehensive Final Exam.

Homework, Quizzes, and Exams will be done in MyLab Math (MML), which can be accessed via the MML links in the modules.

Homework: There will be 8 MML homework assignments, one for each of the 8 modules.  Students will have 1 or 2 weeks to work on the homework assignments.  Pay close attention to deadlines.  Each homework problem can be attempted 3 times. 

Practice Quizzes: There will be one or two MML practice quizzes for each module.  For example, in Module 1 there will be two practice quizzes to complete.  These are timed quizzes.  Each quiz lasts for one hour and you have one attempt to answer each quiz question.  However, you can start the quiz at your convenience during the week it is available.  Plan out a quiet hour to work on a quiz.  The quizzes are open book and open notes, but you may not leave the quiz screen during this hour.  There will be a total of 12 practice quizzes.

Exams: There will also be a midterm exam and a final exam, both are in MyLab MATH (MML).  Both exams must be taken at a testing center with a proctor.  I recommend taking the exams at the testing center of your local college.  Schedule these in advance.  The exams will be given online, but you must show your work on scratch paper and turn in that to your proctors. The exams are closed book and closed notes, but you may use a calculator.  The final exam is comprehensive.

Class Participation:
Late Policy:

Homework, quizzes, and exams must be completed during the scheduled week.  There are no make-ups or do-overs.

Course Ground Rules

The following two statements (1., 2.) were derived from the TBR System-wide Student Rules document, released January 2012:


Read the document in its entirety here.

1. Standards of Conduct:

  • Students are required to adhere to the same professional, legal and ethical standards of conduct online as on campus. In addition, students should conform to generally accepted standards of "netiquette" while sending e-mail, posting comments to the discussion board, and while participating in other means of communicating online. Specifically, students should refrain from inappropriate and/or offensive language, comments and actions.

2. Review the TN eCampus Academic Integrity/Academic Honesty Policy:

  • In their academic activities, students are expected to maintain high standards of honesty and integrity. Academic dishonesty is prohibited.

Such conduct includes, but is not limited to:

  • an attempt by one or more students to use unauthorized information in the taking of an exam
  • to submit as one's own work, themes, reports, drawings, laboratory notes, computer programs, or other products prepared by another person,
  • or to knowingly assist another student in obtaining or using unauthorized materials.

Plagiarism, cheating, and other forms of academic dishonesty are prohibited.

Students guilty of academic misconduct, either directly or indirectly through participation or assistance, are subject to disciplinary action through the regular procedures of the student’s home institution.  Refer to the student handbook provided by your home institution to review the student conduct policy.

In addition to other possible disciplinary sanctions that may be imposed, the instructor has the authority to assign an "F" or zero for an activity or to assign an "F" for the course.

Other Course Rules:

Students are expected to:

  • Participate in all aspects of the course
  • Communicate with other students
  • Learn how to navigate in Brightspace
  • Keep abreast of course announcements
  • Use the assigned course management (Brightspace) email address rather than a personal email address
  • Address technical problems immediately:
  • Observe course netiquette at all times.

Guidelines for Communications


  • Always include a subject line.
  • Remember without facial expressions some comments may be taken the wrong way. Be careful in wording your emails. Use of emoticons might be helpful in some cases.
  • Use standard fonts.
  • Do not send large attachments without permission.
  • Special formatting such as centering, audio messages, tables, html, etc. should be avoided unless necessary to complete an assignment or other communication.
  • Respect the privacy of other class members


  • Review the discussion threads thoroughly before entering the discussion. Be a lurker then a discussant.
  • Try to maintain threads by using the "Reply" button rather starting a new topic.
  • Do not make insulting or inflammatory statements to other members of the discussion group. Be respectful of other’s ideas.
  • Be patient and read the comments of other group members thoroughly before entering your remarks.
  • Be cooperative with group leaders in completing assigned tasks.
  • Be positive and constructive in group discussions.
  • Respond in a thoughtful and timely manner.


The Tennessee Virtual Library is available to all students enrolled in TN eCampus programs and courses. Links to library materials (such as electronic journals, databases, interlibrary loans, digital reserves, dictionaries, encyclopedias, maps, and librarian support) and Internet resources needed by learners to complete online assignments and as background reading will be included within the course modules. To access the Virtual Library, go to the course homepage and select the Virtual Library link under Course Resources.

Students with Disabilities

Qualified students with disabilities will be provided reasonable and necessary academic accommodations if determined eligible by the appropriate disability services staff at their home institution. Prior to granting disability accommodations in this course, the instructor must receive written verification of a student's eligibility for specific accommodations from the disability services staff at the home institution. It is the student's responsibility to initiate contact with their home institution's disability services staff and to follow the established procedures for having the accommodation notice sent to the instructor.

Syllabus Changes

The instructor reserves the right to make changes as necessary to this syllabus. If changes are necessitated during the term of the course, the instructor will immediately notify students of such changes both by individual email communication and posting both notification and nature of change(s) on the course bulletin board.


The information contained in this syllabus is for general information purposes only. While we endeavor to keep this information up-to-date and accurate, there may be some discrepancies between this syllabus and the one found in your online course. The syllabus of record is the one found in your online course. Please make sure you read the syllabus in your course at the beginning of the semester. Questions regarding course content should be directed to your instructor.

Last Revised on October 24, 2018