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Course Syllabus for Linear Algebra with Applications

This course is designed for students who are majoring in secondary mathematics education, mathematics,
science or engineering. This course provides a thorough treatment of linear algebra using a matrix-oriented
approach. Major topics include: matrices, systems of linear equations, linear transformations, determinants,
eigenvectors and eigenvalues, vector spaces, subspaces, inner product spaces, and orthogonality. Emphasis is
on gaining a deep understanding of the subject matter through the use of technology and application projects;
emphasis is also given to development of algebraic reasoning abilities in analyzing conceptual relationships.
This course addresses specific Sunshine State Standards, subject matter competencies and pedagogy
pertinent to the discipline and required for certification.

1. The student will demonstrate an understanding of matrices and their properties and operations.

2. The student will demonstrate an understanding of systems of linear equations.

3. The student will demonstrate an understanding of linear transformations.

4. The student will demonstrate an understanding of determinants and their properties.

5. The student will demonstrate an understanding of eigenvectors and eigenvalues.

6. The student will demonstrate an understanding of vector spaces, subspaces and inner product

7. The student will demonstrate an understanding of vector orthogonality and its applications.


A. Required Textbooks
Elementary Linear Algebra, 6th ed. (Enhanced edition), Larson & Falvo (2009),
Cengage(Brooks/Cole) Publishers, ISBN-13: 978-1-439-04400-1

B. Supplemental Material
Student Solutions Guide - Elementary Linear Algebra, Larson (2003), Cengage(Brooks/Cole)
Publishers, ISBN-13: 978-0618335688

C. Technology
Graphing calculator

D. Supplies
Paper, pen, pencils

A. School Based Hours Course Requirements
There are no school-based hours for this course

B. Required Assessments

• Tests**
• Final Exam** (Additional Element: 10)

**These assignments must be mastered in order to pass the class. If an assignment does not receive a
grade of C or above, the instructor will work with the student to improve the understanding of the
concept and performance of the assignment. The assignment must be corrected and resubmitted and
cannot receive a grade higher than a C. In the event of proven cheating or plagiarizing on any FEAPs
assignment, the student will, at minimum, receive a non-passing grade, not a withdrawal, for the course.


Course Topics:
• Properties of Matrices
• Operations on Matrices
• Systems of Linear Equations
• Linear Transformations
• Determinants
• Eigenvalues
• Eigenvectors
• Vector Spaces
• Subspaces
• Inner Product Spaces
• Vector Orthogonality
• Applications of Vector Orthogonality


A. COE Syllabus Statements:

B. SPC Syllabus Statements:

Each student must read all topics within this syllabus related to the course (found in
sections I-V) and the content of the syllabus statements common to all COE syllabi
(found in the links under section VI). If the student needs clarification on any items in
the syllabus or linked statements, he/she should contact the course instructor.

Larson Linear Algebra, 6th edition
Assigned Problems

eoo means every other odd

For each test unit, up to 3 proofs of even numbered problems given after the last assignment number may
be turned in for extra credit as well.

Section Problems
1.2 1-36 odd, 43-49 odd
1.3 9, 13, 19, 21, 25
2.1 1-51 odd
2.2 1-43 odd
2.3 1-43 odd
2.4 1-57 odd
2.5 1, 3, 5, 7 15, 19, 27, 31-43 odd
Test 1  
3.1 1-37 eoo, 41-61 odd
3.2 1-51 odd
3.3 1-19 odd, 23-41 odd, 45-61 odd
3.4 1-25 odd
3.5 1-57 odd
Test 2  
4.1 1-63 odd
4.2 1-35 odd
4.3 1-35 odd
4.4 1-51 odd
4.5 1-75 eoo
4.6 1-51 odd
4.7 1-39 odd
Test 3  
5.1 1-93 eoo
5.2 1-77 eoo
5.3 1-61 odd
5.4 1-35 odd
5.5 1-33 odd, 50-51 odd
Test 4  
6.1 1-59 odd
6.2 1-77 eoo
6.3 1-67 odd
6.4 1-25 odd
7.1 1-53 odd
7.2 1-49 odd
7.3 1-35 odd
7.4 1-11 odd
Test 5