English | Español

Try our Free Online Math Solver!

Online Math Solver












Please use this form if you would like
to have this math solver on your website,
free of charge.


Course description:
Topics include matrices and linear transformations , abstract vector spaces and subspaces,
linear independence and bases, determinants, systems of linear equations, and eigenvalues and

Text: Larson & Falvo, Elementary Linear Algebra, 6th ed., Houghton Mifflin, 2009

Prerequisite course: Math 8 (Calculus 2)

Prerequisite skills: Upon enrolling in Math 13 at SMC, it is your responsibility to know how to:

Solve systems of linear equations using Gaussian elimination.
• Write the equation of a line in parametric form.
• Prove mathematical statements by methods including proof by contradiction and mathematical induction.
• Integrate and differentiate functions including functions defined by infinite series.
• Evaluate, manipulate, and interpret summation notation .
• Prove algebraically the existence of the inverse of a function by formally proving the function is one-to-
• Be eligible for English 1.

Exit skills / Course objectives: Upon successful completion of Math 13, you should be able to:

• Apply the concepts and theorems of linear algebra to show the consequences of a given definition.
• Perform matrix computations and apply matrix algebra.
• Express a matrix as a product of elementary matrices and an upper triangular matrix.
• Compute the inverse, if possible, of a square matrix , and express it as a product of elementary matrices.
• Solve any size system of linear equations using Gaussian elimination, and, where necessary, express solutions
using parameters or as a linear combination of basis vectors.
• Apply fundamental determinant theorems.
• Prove whether or not a set and operations form a vector space (or subspace).
• Apply the concepts of linear independence and spanning to find a basis for a vector space.
• Prove whether or not a function between two vector spaces is a linear transformation or isomorphism.
• Find the matrix representation of a linear transformation with respect to two given ordered bases .
• Express the kernel and range of a linear transformation as a span of basis vectors.
• Compute the eigenvalues for a matrix, find a basis for the corresponding eigenspaces, and where
possible, diagonalize the matrix.
• Use the Gram-Schmidt process to compute an orthonormal basis of a space.

Attendance: You are responsible for all material covered and all announcements and assignments made at each
class, whether you are present or not. Therefore I recommend that you share contact information with at least
one other student in this class, so that you can find out what you missed in the event of an absence. Students
who do not attend each class meeting of the first week may be withdrawn. Unexcused absences may result in
your being withdrawn from the course. It is your responsibility to withdraw from the course if you wish to do so.

Email:  Here are the rules that apply when sending me email for this purpose:

(1) To ensure that I distinguish your email from unsolicited spam, you must send the message using an
SMC student email address .
(2) You must include the course designation “Math 13” in the subject line, and your first and last name
and SMC ID number in the body of the email.
(3) You may send me an email only to ask questions about the course material.
(4) Please do not send attachments.

Email messages that do not follow these rules may be deleted without being read and do not guarantee a

Classroom Conduct: When in the classroom, you are expected to give your full attention to the lectures and
problem-solving periods. Food, drinks and gum are not allowed in the classroom. Please do not use or check
cell phones, pagers, text messaging or recording devices, headphones or any other electronic device when class
is in session. When you come to class, please turn off such devices, put them into a bag, close the bag, and
place the bag on the floor. Failure to respect this instruction may result in your removal from the

Each student has the right to feel comfortable asking questions, making mistakes and offering good guesses and
correct solutions. Students learn at different rates and prefer a variety of instruction methods. Please be
courteous to and respectful of your classmates and myself.

Dr. Nestler – Math 13 - Homework Guidelines and Checklist

Your goal when answering homework problems is to explain your correct solution carefully. In general,
solutions you see during the lecture are models for your work. In order for an assignment to be eligible for
full credit, make sure it satisfies the following checklist.

Does your completed homework assignment:

• Clearly restate the problem to be solved?
• Define all variables and symbols that are not in the problem as stated?
• Contain justifications of each step of your arguments ?
• Use correctly spelled English words, mathematical notation, punctuation and grammar?
• Solve the question that was originally asked?
• Have a metal staple if it contains more than one page?

Appearance: Rewrite or type your solutions neatly. You may find that you rewrite your solutions more than once.
Use paper that has a clean edge rather than paper ripped out of a notebook, having a ragged edge. If you
have crossed out writing that was not part of your final solution, you should recopy that solution neatly and turn
that in instead.

True/False Questions and Answers:
For true/false questions, if the statement is true, then you must find a
general reason why this is so. A specific example is not sufficient, but a theorem and page number from the
book, or a statement such as, “You proved it in class,” will suffice. If a statement is false, then you must find a
specific example that disproves the statement; this is known as a counterexample.

Plagiarism: While I encourage you to work with others, you must write up your solutions in your own words.
You must give proper reference and credit to others. Examples: “I worked with John on this”; “This example
was Joan’s idea.” Submitting someone else’s work as your own is known as plagiarism and is a form of
cheating that is a serious violation of the college’s Code of Academic Conduct. It is cheating to let someone
else in the class borrow your work for the purpose of copying all or part of it. It is cheating to borrow someone
else’s work for the purpose of copying all or part of it.

A final comment:
You should take pride in your proofs and solutions. Take care to make sure they are legible,
complete and correct. The reader thanks you, and you will be grateful as well when you are studying for an
exam and wish to review your previous work.

Important College Policies

Withdrawal Policy: It is your responsibility to make sure that all conditions of eligibility are met. According to
the schedule of classes, Monday, October 26 is the last day to withdraw from a class with a guaranteed W.
From then until Monday, November 23, a student with extenuating circumstances making withdrawal necessary
may ask the instructor to be withdrawn with a W. In my opinion, any such circumstances would make it
necessary for you to drop and stay withdrawn from all classes at SMC for the remainder of the term. It is
extremely unlikely that students will be dropped from this class after October 26. You should consider
October 26 the last day to withdraw from this class with a W.
Withdrawn students will not be readmitted
except in case of administrative error. Auditing classes (attending while not enrolled) is not permitted.

Codes of Conduct: All SMC students are required to affirm their commitment to the College Honor Code. As
testament to your commitment and readiness to join the Santa Monica College academic community, you and all
students are expected to uphold the Honor Code. By enrolling in courses at SMC, you are certifying the
following statement:

In the pursuit of the high ideals and rigorous standards of academic life, I commit myself to
respect and uphold the Santa Monica College Honor Code, Code of Academic Conduct, and Student
Conduct Code. I will conduct myself honorably as a responsible member of the SMC community in all
endeavors I pursue.

I will vigorously pursue any suspected cases of plagiarism or cheating or other violations of the SMC Code of
Academic Conduct, whether completed or merely attempted. An occurrence of academic dishonesty will result
in an exam score of zero or even a grade of F in the course, and an Academic Dishonesty Report form will be
filed with the Campus Disciplinarian. If your cell phone makes a sound in class, then you may be removed from
the classroom and you may receive a disciplinary sanction for violating the SMC Student Conduct Code.

Some information for me

Please fill out this entire page and return this entire syllabus to me by Wednesday, September 9 in order
to remain enrolled.
You may obtain another copy of this syllabus from our class homepage.

Print your name:

SMC ID number:

Have you enrolled in this course before? If yes, when?

How did you place yourself in this course? Circle one of these four options:

• Grade of C or better in Math 8 at SMC
o If yes, please give your grade, teacher’s name and when you took it:

• Grade of C or better in a Calculus 2 course at another school
o If yes, please give the school’s name and your grade:

• SMC Math Assessment Test
o If yes, when did you take the test?

• Counselor waiver
o If yes, please explain why you have a waiver:

When did you last complete a math class (examples: “Spring 2009,” “Three years ago”), and what was it?

How many units of college coursework are you taking this term?

If you are employed, how many hours are you working at your job each week, on average?

Are you enrolled in high school?

Prev Next