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MAT 288 Linear Algebra

This course is a study of linear equations, determinants, vector spaces, linear transformations, eigenvalues, and eigenvectors.

Credits

4

Prerequisite

Prerequisite: MAT 282

See Course Syllabus

Course Number and Title:

MAT 288 Linear Algebra

Campus Location

  • Dover
  • Georgetown
  • Stanton
  • Wilmington

Prerequisites

Prerequisite: MAT 282

Course Credits and Hours

4 credit(s)

4 lecture hours/week

1 lab hours/week

Course Description

This course is a study of linear equations, determinants, vector spaces, linear transformations, eigenvalues, and eigenvectors.

Additional Materials

Mathematica, Graphing Calculator: TI 83 or TI 84

Required Text(s)

Obtain current textbook information by viewing the campus bookstore - https://www.dtcc.edu/bookstores online or visit a campus bookstore. Check your course schedule for the course number and section.

Disclaimer

None

Core Course Performance Objectives (CCPOs)

  1. Perform and apply matrix operations. (CCC 2, 6)
  2. Use determinants to solve systems of equations and applied problems. (CCC 2, 6)
  3. Perform operations on vector spaces. (CCC 2, 6)
  4. Represent linear transformations using matrices and perform basic operations on linear transformations. (CCC 2, 6)
  5. Find and apply eigenvalues and eigenvectors for matrices. (CCC 2, 6)

See Core Curriculum Competencies and Program Graduate Competencies at the end of the syllabus. CCPOs are linked to every competency they develop.

Measurable Performance Objectives (MPOs)

Upon completion of this course, the student will:

  1. Perform and apply matrix operations.
    1. Perform basic operations on matrices.
    2. Apply the operations of inverse, transposition, and factorization to matrices.
    3. Solve application problems using Gaussian elimination.
    4. Prove theorems involving matrix algebra.
  2. Use determinants to solve systems of equations and applied problems.
    1. Perform cofactor expansion.
    2. Apply Cramer's rule.
    3. Solve applied problems using properties of determinants.
    4. Prove theorems involving determinants.
  3. Perform operations on vector spaces.
    1. Perform vector operations, including add, subtract, multiply, scale, dot product, norm, distance, and projections.
    2. Define a vector space and subspace.
    3. Construct a basis for a given vector space, and state its dimension.
    4. Determine the rank and nullity of a given vector space.
    5. Calculate projections and orthogonality among Euclidean vectors, including the Gram-Schmidt orthonormalization process and orthogonal matrices.
    6. Prove linear independence or dependence of a set of vectors.
  4. Represent linear transformations using matrices and perform basic operations on linear transformations.
    1. Define linear transformation.
    2. Determine the kernel, nullity, range, and rank of a given linear transformation.
    3. Perform linear transformations on vectors.
    4. Prove or disprove linear transformations.
  5. Find and apply eigenvalues and eigenvectors for matrices.
    1. Determine the eigenvalues and eigenvectors of a given matrix.
    2. Solve systems using eigenvalues.
    3. Determine the characteristic polynomial of a matrix.
    4. Determine whether matrices are similar.
    5. Determine if a given matrix is diagonalizable.
    6. Prove theorems involving eigenvalues and vectors.

Evaluation Criteria/Policies

The grade will be determined using the Delaware Tech grading system:

90-100 = A
80-89 = B
70-79 = C
0-69 = F
Students should refer to the Catalog/Student Handbook for information on the Academic Standing Policy, the Academic Integrity Policy, Student Rights and Responsibilities, and other policies relevant to their academic progress.

Final Course Grade

Calculated using the following weighted average

Evaluation Measure

Percentage of final grade

4 Tests (summative) (equally weighted)

70%

Labs / Projects (formative)

10%

Formative (quizzes, activities)

10%

Homework (formative)

10%

TOTAL

100%

Core Curriculum Competencies (CCCs are the competencies every graduate will develop)

  1. Apply clear and effective communication skills.
  2. Use critical thinking to solve problems.
  3. Collaborate to achieve a common goal.
  4. Demonstrate professional and ethical conduct.
  5. Use information literacy for effective vocational and/or academic research.
  6. Apply quantitative reasoning and/or scientific inquiry to solve practical problems.

Students in Need of Accommodations Due to a Disability

We value all individuals and provide an inclusive environment that fosters equity and student success. The College is committed to providing reasonable accommodations for students with disabilities. Students are encouraged to schedule an appointment with the campus Disabilities Support Counselor to request an accommodation needed due to a disability. The College's policy on accommodations for persons with disabilities can be found in the College's Guide to Requesting Academic Accommodations and/or Auxiliary Aids Students may also access the Guide and contact information for Disabilities Support Counselors through the Student Resources web page under Disabilities Support Services, or visit the campus Advising Center.

Minimum Technology Requirements

Minimum technology requirements for online, hybrid, video conferencing and web conferencing courses.

Academic Integrity

https://dtcc.smartcatalogiq.com/Current/Catalog/Academics/Academic-Integrity

Attendance

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Cell phone/Electronic Device

https://dtcc.smartcatalogiq.com/Current/Catalog/Student-Policy/Cell-Phone-and-Electronic-Device-Policy

Tuition Adjustment Policy

https://dtcc.smartcatalogiq.com/Current/Catalog/Financial/Tuition-Fee-Adjustment-Policy-Course-or-Semester-Withdrawal