Math 2318: Linear Algebra

Spring 2018

Synonym: 30932, Section: 001, Northridge 2244
Monday / Wednesday 6:00 pm- 7:20 pm

Course Content:

Course Description: MATH 2318 LINEAR ALGEBRA A study of linear equations, linear transformations, matrices, determinants, finite-dimensional vector spaces, and quadratic forms. Prerequisites: MATH 2415 or its equivalent.

Instructional Methodology: This course is taught in the classroom primarily as a lecture/discussion course. Course Rationale:


Please make sure you have the necessary prerequisites for this course. That means you need a C or better in Calculus III (or an equivalent course). If I feel you are not prepared for this course, I may choose to withdraw you. If you have any questions about your preparation for the course, please come and talk to me about it.

Course Materials:

Text: Linear Algebra, A Geometric Approach, 2nd edition, by Theodore Shifrin & Malcolm R. Adams, W. H. Freeman & Co, 2011 (ISBN-13: 978-1-4292-1521-3, ISBN-10: 1-4292-1521-6).

Technology:  The use of calculators or computers in order to perform routine computations is encouraged in order to give students more time on abstract concepts.  Mathematica software is available for student use.  You may be required to use Mathematica software for the course; you may choose to purchase this (there is a student editionand various time-limited versions available at a reduced price), but you are not required to do so.  This software is available in the classrooms and in the Learning Labs.


There will be 3 exams plus a final exam (part of which will be comprehensive).  In addition, you will be assigned several computer labs which will count for a substantial grade.  Grades will be weighted as follows:


Tests 1, 2, 3




Final Exam



Homework/quizzes/computer assignments



If you take any test late for any reason, there will be a penalty of 10 points off your test grade. However, no late tests will be allowed after I hand the graded tests back in class.  If you miss a test, you must try to take it during this “late” period.  If you do not take the test during that period, you will receive a 0 for that grade.  In that case, you will need to take the make-up exam to replace that 0. 

Grades will be assigned as follows:

A :

90% or better and a grade of at least 80% on the final

D :

60% - 69%

B :

80% - 89% and a grade of at least 70% on the final

F :

below 60%

C :

70% - 79% and a grade of at least 60% on the final


W :

Withdrawn by student or instructor prior to last withdrawal date on school calendar

I :

Incomplete grades (I) will be given only in very rare circumstances. Generally, to receive a grade of "I", a student must have taken all tests, be passing, and after the last date to withdraw, have a personal tragedy occur which prevents course completion. An incomplete grade cannot be carried beyond the established date in the following semester. The completion date is determined by the instructor but may not be later than the final deadline for withdrawal in the subsequent semester.


It is the student's responsibility to initiate all withdrawals in this course.  The instructor may withdraw students for excessive absences (4) but makes no commitment to do this for the student. After the last day to withdraw, neither the student nor the instructor may initiate a withdrawal. It is the responsibility of each student to ensure that his or her name is removed from the roll should he or she decide to withdraw from the class.  The instructor does, however, reserve the right to drop a student should he or she feel it is necessary. The student is also strongly encouraged to retain a copy of the withdrawal form for their records.

Students who enroll for the third or subsequent time in a course taken since Fall, 2002, may be charged a higher tuition rate, for that course. State law permits students to withdraw from no more than six courses during their entire undergraduate career at Texas public colleges or universities.  With certain exceptions, all course withdrawals automatically count towards this limit.  Details regarding this policy can be found in the ACC college catalog.

The withdrawal deadline for Spring 2018 is April 23, 2018.


You should bring your homework to class every day.  It will be collected regularly.  There may also be in-class assignments or quizzes collected for a grade (as part of your homework grade). There will be a penalty on late homework. Homework that is more than a week late might not receive any credit.  If you do not follow the instructions that will be announced in class about how to organize and submit your homework, you may not receive full (or any) credit for it.

Classroom behavior:

Classroom behavior should support and enhance learning. Behavior that disrupts the learning process will be dealt with appropriately, which may include having the student leave class for the rest of that day. In serious cases, disruptive behavior may lead to a student being withdrawn from the class. ACC's policy on student discipline can be found in the Student Handbook on the web at:

Class participation:

All students are expected to actively participate in this class. This can include asking relevant questions in class, participating in class discussions and other in-class activities, helping other students, coming to office hours with questions, and doing other things that contribute to the class.

Keeping up:

Please, try to keep up with the homework and with the lecture in class. There just isn't much time to catch up. This means you have to be sure to allow yourself plenty of time to do the homework and to study.

Ask questions:

Please, please, please, if you don't understand something, or you aren't clear about something, or if you think I (or the book) have made a mistake (it has been known to happen), or if you have any other questions, please ask. Don't let confusion accumulate. If you don't want to ask in class, come to our office hours (or call) and ask. It is much easier to ask a question now than to miss it on the test.  I expect all students to participate in class discussions and other activities. Trust me, you will get much more out of the class if you become actively involved in it.

Always show your work:

It is much more important that you understand the processes involved in solving problems than that you just give me the right answer. If I see from your work that you understand what you are doing, I will usually give partial credit for a problem, even if you made a mistake somewhere along the line. If you don't show your work (unless I believe you could reasonably do it in your head), I may not give you full credit, even if the answer is right. If you can really do something in your head, that's great, but when in doubt, write it down.  It is also very important that you write what you mean. I will correct your notation the first few times, but I will start counting it wrong if you continue to write things incorrectly. In addition, please write clearly and legibly. If I can't read it, I won't grade it.

Time required and outside help:

To do homework and study requires two or three times as much time outside of class as the time you spend in class in order to succeed in this course. If you need more out-of-class help than you can obtain in your instructor's office hours, free tutoring is available in any of ACC's Learning Labs.

ACC main campuses have Learning Labs which offer free first-come, first-serve tutoring in mathematics courses. The locations, contact information and hours of availability of the Learning Labs are posted at:


Linear Algebra, MATH 2318, Learning Outcomes

Upon successful completion of this course, students will:

1.         Solve systems of linear equations using multiple methods, including Gaussian elimination and matrix inversion.

2.         Carry out matrix operations, including inverses and determinants.

3.         Demonstrate understanding of the concepts of vector space and subspace.

4.         Demonstrate understanding of linear independence, span, and basis.

5.         Determine eigenvalues and eigenvectors and solve eigenvalue problems.

6.         Apply principles of matrix algebra to linear transformations.

7.         Demonstrate understanding of inner products and associated norms.

Course Objectives

The course objectives of Linear Algebra are:

1.      To use mathematically correct language and notation for Linear Algebra.

2.      To become computational proficiency involving procedures in Linear Algebra.

3.      To understand the axiomatic structure of a modern mathematical subject and learn to construct simple proofs.

4.      To solve problems that apply Linear Algebra to Chemistry, Economics and Engineering.

The topics that will enable this course to meet its objectives are:

(i)             the basic arithmetic operations on vectors and matrices, including inversion and determinants, using technology where appropriate;

(ii)           solving systems of linear equations, using technology to facilitate row reduction;

(iii)          the basic terminology of linear algebra in Euclidean spaces, including linear independence, spanning, basis, rank, nullity, subspace, and linear transformation;

(iv)          the abstract notions of vector space and inner product space;

(v)           finding eigenvalues and eigenvectors of a matrix or a linear transformation, and using them to diagonalize a matrix;

(vi)          projections and orthogonality among Euclidean vectors, including the Gram-Schmidt orthonormalization process and orthogonal matrices;

(vii)        the common applications of Linear Algebra, possibly including Markov chains, areas and volumes, Cramer's rule, the adjoint, and the method of least squares;

(viii)       the nature of a modern mathematics course: how abstract definitions are motivated by concrete examples, how results follow from the axiomatic definitions and are specialized back to the concrete examples, and how applications are woven in throughout. This course will present various "characterization" theorems (eg. characterizing isomorphic finite-dimensional vector spaces by their dimension and characterizing invertible matrices by various criteria);

(ix)          basic proof and disproof techniques, including mathematical induction, verifying that axioms are satisfied, standard "uniqueness" proofs, proof by contradiction, and disproof by counterexample.

ACC College Policies

Statement on Scholastic Dishonesty - A student attending ACC assumes responsibility for conduct compatible with the mission of the college as an educational institution.  Students have the responsibility to submit coursework that is the result of their own thought, research, or self-expression.  Students must follow all instructions given by faculty or designated college representatives when taking examinations, placement assessments, tests, quizzes, and evaluations.  Actions constituting scholastic dishonesty include, but are not limited to, plagiarism, cheating, fabrication, collusion, and falsifying documents.    Penalties for scholastic dishonesty will depend upon the nature of the violation and may range from lowering a grade on one assignment to an “F” in the course and/or expulsion from the college.  See the Student Standards of Conduct and Disciplinary Process and other policies at

Student Rights and Responsibilities - Students at the college have the rights accorded by the U.S. Constitution to freedom of speech, peaceful assembly, petition, and association. These rights carry with them the responsibility to accord the same rights to others in the college community and not to interfere with or disrupt the educational process. Opportunity for students to examine and question pertinent data and assumptions of a given discipline, guided by the evidence of scholarly research, is appropriate in a learning environment. This concept is accompanied by an equally demanding concept of responsibility on the part of the student. As willing partners in learning, students must comply with college rules and procedures.

Statement on Students with Disabilities - Each ACC campus offers support services for students with documented disabilities. Students with disabilities who need classroom, academic or other accommodations must request them through Student Accessibility Services (SAS, formerly OSD).  Students are encouraged to request accommodations when they register for courses or at least three weeks before the start of the semester, otherwise the provision of accommodations may be delayed.

Students who have received approval for accommodations from SAS for this course must provide the instructor with the ‘Notice of Approved Accommodationsfrom SAS before accommodations will be provided.  Arrangements for academic accommodations can only be made after the instructor receives the ‘Notice of Approved Accommodationsfrom the student.

Students with approved accommodations are encouraged to submit the ‘Notice of Approved Accommodationsto the instructor at the beginning of the semester because a reasonable amount of time may be needed to prepare and arrange for the accommodations.  Additional information about Student Accessibility Services is available at  HYPERLINK ""

Safety Statement - Austin Community College is committed to providing a safe and healthy environment for study and work. You are expected to learn and comply with ACC environmental, health and safety procedures and agree to follow ACC safety policies. Additional information on these can be found at Because some health and safety circumstances are beyond our control, we ask that you become familiar with the Emergency Procedures poster and Campus Safety Plan map in each classroom. Additional information about emergency procedures and how to sign up for ACC Emergency Alerts to be notified in the event of a serious emergency can be found at

Please note, you are expected to conduct yourself professionally with respect and courtesy to all. Anyone who thoughtlessly or intentionally jeopardizes the health or safety of another individual will be dismissed from the days activity, may be withdrawn from the class, and/or barred from attending future activities.

You are expected to conduct yourself professionally with respect and courtesy to all. Anyone who thoughtlessly or intentionally jeopardizes the health or safety of another individual will be immediately dismissed from the days activity, may be withdrawn from the class, and/or barred from attending future activities.

Use of ACC email - All College e-mail communication to students will be sent solely to the students ACCmail account, with the expectation that such communications will be read in a timely fashion. ACC will send important information and will notify you of any college related emergencies using this account.  Students should only expect to receive email communication from their instructor using this account.  Likewise, students should use their ACCmail account when communicating with instructors and staff.  Instructions for activating an ACCmail account can be found at

Testing Center Policy - Under certain circumstances, an instructor may have students take an examination in a testing center.  Students using the Academic Testing Center must govern themselves according to the Student Guide for Use of ACC Testing Centers and should read the entire guide before going to take the exam.  To request an exam, one must have:

·    ACC Photo ID

·    Course Abbreviation (e.g., ENGL)

·    Course Number (e.g.,1301)

·    Course Synonym (e.g., 10123)

·    Course Section (e.g., 005)

·    Instructor's Name

Do NOT bring cell phones to the Testing Center.  Having your cell phone in the testing room, regardless of whether it is on or off, will revoke your testing privileges for the remainder of the semester.  ACC Testing Center policies can be found at

Student And Instructional Services - ACC strives to provide exemplary support to its students and offers a broad variety of opportunities and services.  Information on these services and support systems is available at: Links to many student services and other information can be found at: For help setting up your ACCeID, ACC Gmail, or ACC Blackboard, see a Learning Lab Technician at any ACC Learning Lab.

Concealed Handgun Policy - The Austin Community College District concealed handgun policy ensures compliance with Section 411.2031 of the Texas Government Code (also known as the Campus Carry Law), while maintaining ACC’s commitment to provide a safe environment for its students, faculty, staff, and visitors. Beginning August 1, 2017, individuals who are licensed to carry (LTC) may do so on campus premises except in locations and at activities prohibited by state or federal law, or the college’s concealed handgun policy. It is the responsibility of license holders to conceal their handguns at all times. Persons who see a handgun on campus are asked to contact the ACC Police Department by dialing 222 from a campus phone or 512-223-7999.Refer to the concealed handgun policy online at

Course Outline and Approximate Calendar:
Please note:  schedule changes may occur during the semester.
Any changes will be announced in class.
This is a pretty optimistic schedule, so there is a good chance we may have to drop a section or two…







Holiday - no class








The dot product




Hyperplanes in Rn




Gaussian elimination




Theory of linear systems








Matrix operations

Test 1 – Dates to be announced in class



2.2, 2.3

Linear transforms and inverse matrices




Elementary matrices



2.5, 3.1

The transpose and subspaces of Rn




The four fundamental subspaces




Linear independence and basis




Dimension and its consequences




Dimension and its consequences




Abstract vector spaces

Test 2 – Dates to be announced in class

SPRING BREAK:  3/12/18 - 3/18/18




Inconsistent systems and projection




Orthogonal bases




The matrix of a linear transform and the change of base formula




Linear transforms on abstract vector spaces




Properties of determinants




Cofactors and Cramer’s Rule




Signed area in R2 and signed volume in R3




The characteristic polynomial

Test 3 – Dates to be announced in class








More applications




The spectral theorem




Computer graphics and geometry




Matrix exponentials and differential equations







Final Exam, Part 1



Final Exam, Part 2


This webpage was created by Marcus McGuff.
It was last updated on January 8, 2018 .