# Introduction to Linear Algebra

**Text**

Elementary Linear Algebra, 6^{th} Edition by Larson, Edwards and Falvo.

**Prerequisite
**Math 151 with a course grade of ‘C’ or better, or equivalent.

**Course Description
**This course serves as an introduction to the theory and applications of
elementary linear

algebra, and is the basis for most upper division courses in mathematics. The topics covered

in this course include matrix algebra, Gaussian Elimination, systems of equations,

determinants, Euclidean and general vector spaces, linear transformations, orthogonality and

inner product spaces, bases of vector spaces, the change of basis theorem, eigenvalues and

eigenvectors, the rank and nullity of matrices and of linear transformations. This course is

intended for the transfer student planning to major in mathematics, physics, engineering,

computer science, operational research, economics, or other sciences.

**Learning Objectives
**Upon successful completion of the course the student will be able to:

1. Solve systems of linear equations using several algebraic methods.

2. Construct and apply special matrices, such as symmetric, skew-symmetric, diagonal,

upper triangular or lower triangular matrices.

3. Perform a variety of algebraic matrix operations, including multiplication of matrices,

transposes, and traces.

4. Calculate the inverse of a matrix using various methods, and perform application

problems involving the inverse.

5. Compute the determinant of square matrices and use the determinant to determine

existence of an inverse.

6. Derive and apply algebraic properties of determinants.

7. Perform vector operations on vectors from Euclidean Vector Spaces including vectors

from ≺ .

8. Compute the equations of lines and planes and write these in their corresponding

vector forms.

9. Perform linear transformations in Euclidean vector spaces, including basic linear

operators, and determine the standard matrix of the linear transformation.

10. Prove whether a given structure is a vector space and determine whether a given

subset of a vector space is itself a vector space.

11. Determine if a set of vectors spans a space, and if such a set is linearly dependent or

independent.

12. Determine if a set of functions is linearly independent using various techniques

including calculating the determinant of the Wronskian.

13. Solve for the basis and the dimension of a vector space.

14. Determine the rank, the nullity, the column space and the row space of a matrix.

15. Describe orthogonality between vectors in an abstract vector space by means of an

inner product, and compute the inner product between vectors of a this inner product

space.

16. Compute the QR-decomposition of a matrix using the Gram-Schmidt process.

17. Perform changes of bases for a vector space, including computation of the transition

matrix and determining an orthonormal basis for the space.

18. Compute all the eigenvalues of a square matrix, including any complex eigenvalues,

and determine their corresponding eigenvectors.

19. Determine if a square matrix is diagonalizable and compute the diagonalization of a

matrix whose eigenvalues are easily calculated.

20. Perform linear transformations among abstract general vector spaces, determining the

rank, the nullity and the associated matrix of the transformation.

**Course Goal
**Upon successful completion of this course the student will be ready to apply
the

principles of Linear Algebra to the study of Differential Equations and apply their knowledge

to applications in science, computer science and/or economics. To fulfill the course

objectives, we will cover the material from Chapters 1 through 7 in the textbook.

**Academic Success
**Remember that the formula for academic success requires at least four hours
of

preparation, study, and review for each hour spent in the classroom.

An adequate plan of study will include the following:

Before class: read the material to be covered in the text

In Class: Take notes, ask questions, work examples yourself rather than copy

them.

After Class: Rewrite your notes, reread the text, do all the suggested

assignments the day they are assigned, and go back and review older material

regularly.

Correctly written test, quiz, and homework problems and
exercises in mathematics,

whether they are ‘pure’ math or application problems, should have the following
qualities:

They should be well organized and neatly written.

They should show all relevant work to support the solution.

The final answer is correct (and includes correct units if applicable) Circle or

underline your final answers.

**Personal Learning Assistance Center
**The PLACe is a tutoring center on the Miramar campus which will provide free
tutoring

in many languages. They provide for walk-in tutoring as well as structured lessons. If you

feel you are falling behind or are having difficulty understanding the material of the class,

please make sure that you utilize this free campus service.

The PLACe's mission is to provide quality and timely
learning support services to all

Miramar students by means of:

• exceptional individualized, group and computer assisted
tutorials;

• strong alliances with Miramar faculty and programs;

• an environment that is inclusive, comprehensive, safe and that removes all
barriers to

learning;

• opportunities for competent and motivated students to learn the benefits of
helping

others through peer tutoring.

**DSPS
**Be aware that DSPS exists to help students with verified disabilities who
may require

special accommodations. Students are encouraged to contact Disability Support Programs

and Services Office in the early stages of their college planning. Any student currently

registered with DSPS and requiring an accommodation is required to contact the instructor

and acquaint them with the circumstances.

**Grading Policies**

a. Homework: At the end of each class, homework will be
assigned. You should

study the section carefully, working through examples and rereading each
definition

and theorem before beginning the assigned exercises. There will be an
opportunity to

ask questions about the homework at the beginning of each class.

b. Quizzes: There will be 6 quizzes during the semester.
Each quiz will be graded on

a 30 point scale using the criteria above. The lowest quiz score will be
dropped. The

quizzes will count for 150 points of the final grade.

c. Tests: There will be three exams during the session,
with approximately the

following coverage:

Test 1 Chapters 1 – 3

Test 2 Chapters 4 – 5

Test 3 Chapters 6 – 7

Each exam will be worth 100 points for a total of 300 points of the final grade.

d. Final Examination: The final exam, administered on the
last class date, 19

May. It will be cumulative. The final exam will be worth a total of 150 points
of the

final grade.

e. Grading Scale: Expect the grading scale for the course to be as follows:

0 – 239 points F

360 – 419 points D

420 – 479 points C

480 – 539 points B

540 – 600 points A

**Attendance
**Students may be dropped for nonattendance (missing 4 or more classes) up to
the

final date to withdraw from the class. If you stop attending this class it is your responsibility to

drop the course yourself. If you decide to drop, you do not need any signatures. If you must

miss a class, please inform me beforehand (email is usually most convenient) and realize

that it is your responsibility to make up any missed class work. It will not be practical to make

up tests so you should plan on attending each class session.

It is expected that students will arrive on time for class
and prepared to work. You

should make certain to eat breakfast before class so that you will not be
distracted during the

class itself. If you habitually arrive late for class, take long breaks, or
leave class early, these

will be counted as absences.

o It is the student’s responsibility to drop all classes
in which he/she is no longer

attending.

o It is the instructor’s discretion to withdraw a student after the add/drop
deadline (see

college course schedule) due to excessive absences.

o Student’s who remain enrolled in a class beyond the published withdrawal
deadline, as

stated in the class schedule, will receive an evaluative letter grade in the
class.

**Academic integrity and behavior
**Aside from tests and the final exam, you may work together outside of class
with

whomever you wish. During tests and quizzes I expect that you will do your own work using

only materials which I have specified. You have been placed in a position of responsibility

and trust in this regard and it is expected that you will honor your obligation. As a minimum

penalty an individual who fails to honor their obligation during a testing process shall receive

a zero for the test indicated. A second occurrence shall result in a failing grade for the

course. Any such instance shall be reported to the school for action as appropriate.

If there are special circumstances which may affect your
performance in this class, or

of which you believe I should be informed, please do so at your earliest
convenience.

You are responsible for the policies outlined in this
syllabus. These policies may be

subject to modification as the semester progresses. Thank you and have a
successful

semester.