Skagit Valley College logo

Catalog Course Search Details

 Course Title:   Elementary Linear Algebra

 Title Abbreviation:   LINEAR ALGEBRA

 Department:    MATH

 Course #:    204

 Credits:    5

 Variable:     No

 IUs:    5

 CIP:    270101

 EPC:    n/a

 REV:    2014

 Course Description  

An introductory course including systems of linear equations; matrices; the vector space Rn; determinants, Cramer's Rule; applications.


Prerequisite: MATH& 151 with a grade of C or better.

Additional Course Details

Contact Hours (based on 11 week quarter)

Lecture: 55

Lab: 0

Other: 0

Systems: 0

Clinical: 0

Intent: Distribution Requirement(s) Status:  

Academic Elective  

Equivalencies At Other Institutions

Other Institution Equivalencies Table
Institution Course # Remarks
U of W 205
WWU 204

Learning Outcomes

After completing this course, the student will be able to:

  1. Perform Gauss-Jordan elimination to solve a system of equations.
  2. Transform a matrix to row-reduced echelon form.
  3. Use Cramer??s Rule to solve a system of equations.
  4. Test for independence/dependence in R??.
  5. Reduce a spanning set to a basis in R??.
  6. Extend an independent set to a basis in R??.
  7. Find a basis for the solution space Ax=0.
  8. Perform the Gram-Schmidt process (optional).
  9. Compute a basis for the kernel of a linear transformation.
  10. Compute a basis for the image of a linear transformation.
  11. Find eigenvalues and corresponding eigenvectors of a matrix.
  12. Orthogonally diagonalize a symmetric matrix.
  13. Use the process of linear algebra to solve application problems.
  14. Apply alternative mathematical techniques, from a historical perspective where appropriate.
  15. Understand how mathematics is used in other fields and occupations.
  16. Understand the use of mathematics cross-culturally.

General Education Learning Values & Outcomes

Revised August 2008 and affects outlines for 2008 year 1 and later.

1. Information Literacy

Definition: Recognizing when information is needed and have the ability to locate, evaluate, and use effectively the needed information.

Outcomes: Students will be able to . . .
1.1 Determine the extent of information needed.

2. Critical Thinking

Definition: The ability to think critically about the nature of knowledge within a discipline and about the ways in which that knowledge is constructed and validated and to be sensitive to the ways these processes often vary among disciplines.

Outcomes: Students will be able to . . .
2.1 Identify and express concepts, terms, and facts related to a specific discipline.
2.3 Identify, interpret, and evaluate pertinent data and previous experience to reach conclusions.
2.7 Identify and evaluate connections and relationships among disciplines.
2.9 Apply and/or create problem-solving strategies to successfully adapt to unpredictable and/or changing environments.

8. Mathematical Reasoning

Definition: Understanding and applying concepts of mathematics and logical reasoning in a variety of contexts, both academic and non-academic.

Outcomes: Students will be able to . . .
8.1 Analyze problems to determine what mathematical principles apply.
8.2 Correctly apply logical reasoning and mathematical principles to solve problems.
8.3 Interpret information and reasoning expressed mathematically (for example in spreadsheets, diagrams, charts, formulas, etc.).
8.4 Communicate mathematical information effectively.

10. Technology

Definition: Understanding the role of technology in society and using technology appropriately and effectively.

Outcomes: Students will be able to . . .
10.3 Use technology appropriate to the context and task to effectively retrieve and manage information, solve problems, and facilitate communication.

Course Contents

  1. Geometry of R'
  2. Linear equations and Matrices
  3. Determinants
  4. Independence and basis in R??
  5. Linear transformations
  6. Eigenvalues and Eigenvectors
  7. Vector spaces
  8. Applications may include curve fitting, Markov Chains, Kirchoff??s Laws, Leontief Model, Linear Programming