Course Descriptions & Syllabi

Course Descriptions & Syllabi

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Note: some or all of the courses in the subjects marked as "Transfer" can be used towards a transfer degree: Associate of Science and Arts or Associate of Engineering Science at DACC. Transferability for specific institutions and majors varies. Consult a counselor for this information.

Areas of Study | | MATH137 syllabus

COURSE TITLE:Introduction to Linear Algebra

This course is a study of introductory linear algebra. Basic techniques are introduced involving vectors and matrices; vector spaces and subspaces; linear dependence and independence, transformations and dimensionality; determinants; orthogonality; and inner product spaces. MATLAB and Mathematica are utilized as a tools for working with tedious problems.

Place into MATH137 with approved and documented math placement test scores or by completing MATH120 Calculus l with a grade of C or better.

NOTES: This course is a basis for a first undergraduate course in linear algebra. Because linear algebra provides the tools to deal with many problems in fields ranging from forestry to nuclear physics, it is desirable to make the subject accessible to students from a variety of disciplines. There is a blend of intuition and rigor in the presentation. It is anticipated that the student will attain at least 70% accuracy in meeting these objectives.

Students are expected to achieve strong critical thinking skills in terms of problem solving skills. Students are expected to be able to determine from any initial question of any of the following that apply:
  1. the meaning and importance of all given information
  2. the primary unknown for which a solution is desired
  3. all secondary unknowns that will be needed to determine the primary unknown
  4. all formulas and/or theorems that are applicable to a solution, and/or
  5. a proper understanding of the meaning/interpretation of the solution
Upon completion of this course, students will be able to:
  • Clearly show work or provide clear explanation as how to setup and generate a solution for application problems
  • Correctly make use of computer software to provide solution to problems involving large matrix systems
  • Define and explain basic vector terminology in discussions (oral or written)
  • Define and write all required algebraic symbols and abbreviations, primarily those that relate to matrices, vectors, and systems of equations
  • Provide clear explanation to both step-by-step logical setup and solution process for application problems
  • Solve problems by determining, from any initial question, the techniques needed to deconstruct the information provided in a problem as it relates to solution
  • Clearly relate interpretation of solution to give real-world meaning to numeric answers, and to properly interpret abstract answers
Topic Specific Learning Outcomes
  • Calculate the sum and product of matrices
  • Identify the matrix operations
  • Generate the reduced form of an augmented matrix using Gauss-Jordan operations
  • Calculate the inverse of a square matrix
  • solve a linear system of equations via inverse technique
  • distinguish between an independent and a dependent linear system
  • distinguish between linear systems that have no solution, finite solutions, or infinite solutions
  • Calculate stable Markov solutions to iterative processes
  • Calculate determinants for square matrices
  • calculate the determinant of large square matrices from Cofactor Expansion
  • List the properties of determinants
  • simplify matrix expressions
  • Explain the gauss-Jordan row operations
  • simplify matrices prior to determinate calculation
  • List and explain the axioms of Vector Spaces
  • Differentiate between a set of vectors that is a Space and a set of vectors that is not a Space
  • Calculate the dot product of two vectors
  • Calculate the angular measure between two vectors
  • Calculate the magnitude of a vector
  • Distinguish between a vector rule that defines a Subspace and one that does not define a Subspace
  • Generate the linear combination of a set of vectors
  • Distinguish between an independent and a dependent set of vectors
  • Calculate the dimension of a Space
  • Calculate the Rank of a matrix
  • Calculate the projection of one vector onto another
  • Generate the projection of a vector onto a subspace
  • Generate an orthogonal basis from the Gram-Schmidt Orthogonalization process
  • Calculate the eigenvalues and eigenvectors of a square matrix
  • Perform a Linear Transformation on a matrix
  • Generate the kernel and the range of a transformation
  • Distinguish between a Transform that is one-to-one and one that is not
  • Distinguish between a Transform that is invertible and one that is not
  • Generate the coordinate vectors in a linear combination
  • List the axioms defining an inner product space
  • Calculate vector magnitude, as well as distance and angle between vectors in alternate inner product spaces
  • Draw a space-time diagram based on the Minkowski inner product space
  • calculate the Minkowski Inner Product Space time dilation values
  • Apply appropriate technology to find solutions to problems involving large matrix systems

  • Introduction to Linear Systems 12%
    • Matrices and Their Algebra
    • Gauss-Jordan Elimination
    • Basis and Dimension
    • Inverses of Square Matrices
    • The Linear Transformation T (x) = Ax
  • Vector Spaces 20%
    • The Geometry of Rn
    • Vector Spaces
    • Dot Product
    • Linear Combinations and Subspaces
    • Independence
    • Bases, Rank, and Kernel
    • Dimension and Rank
    • Coordinatization of Vectors
    • Linear Transformations
    • Inner Product Spaces
  • Determinants 12%
    • Areas, Volumes, and Cross Products
    • The Determinant of a Square Matrix
    • Computation of Determinants
  • Eigenvalues and Eigenvectors 18%
    • Eigenvalues and Eigenvectors
    • Diagonalization
  • Orthogonality 18%
    • Projections
    • The Gram-Schmidt Process
    • Orthogonal Matrices
  • Linear Transformations and Similarity 16%
    • Properties of Linear Transformations
    • Matrix Representations
    • Change of Basis and Similarity


Linear Algebra with Applications, by Gareth Williams, WCB Publishing, 9th Edition 2019.

See bookstore website for current book(s) at


The student should obtain 70% competency in the above as measured by exams, assignments, and a comprehensive final.

"Assignments" will be 15 items composed of 10 homework sets from the text, 4 homework sets from the instructor, and 1 long term project.

The course grade will be determined by:
Grading Scale:
A= 90-100%
B= 80-89%
C= 70-79%
D= 60-69%
F= Under 60%


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