Course Number and Title: MAT 288 Linear Algebra
This course is a study of linear equations, determinants, vector spaces, linear transformations, eigenvalues, and eigenvectors.
- Perform and apply matrix operations. (CCC 1, 2, 6)
- Use determinants to solve systems of equations and applied problems. (CCC 2, 6)
- Perform operations on vector spaces. (CCC 2, 6)
- Represent linear transformations using matrices and perform basic operations on linear transformations. (CCC 1, 2, 6)
- Find and apply eigenvalues and eigenvectors for matrices. (CCC 1, 2, 6)
See Core Curriculum Competencies and Program Graduate Competencies at the end of the syllabus. CCPOs are linked to every competency they develop.
Upon completion of this course, the student will:
- Perform and apply matrix operations.
- Perform basic operations on matrices.
- Apply the operations of inverse, transposition, and factorization to matrices.
- Solve application problems using Gaussian elimination.
- Prove theorems involving matrix algebra.
- Use determinants to solve systems of equations and applied problems.
- Perform cofactor expansion.
- Apply Cramer’s rule.
- Solve applied problems using properties of determinants.
- Prove theorems involving determinants.
- Perform operations on vector spaces.
- Perform vector operations, including add, subtract, multiply, scale, dot product, norm, distance, and projections.
- Define a vector space and subspace.
- Find the basis and dimension of a given vector space.
- Determine the rank and nullity of a given vector space.
- Calculate projections and orthogonality among Euclidean vectors, including the Gram-Schmidt orthonormalization process and orthogonal matrices.
- Prove linear independence or dependence of a set of vectors.
- Represent linear transformations using matrices and perform basic operations on linear transformations.
- Define linear transformation.
- Determine the kernel, nullity, range, and rank of a given linear transformation.
- Perform linear transformations on vectors.
- Prove or disprove linear transformations.
- Find and apply eigenvalues and eigenvectors for matrices.
- Determine the eigenvalues and eigenvectors of a given matrix.
- Solve systems using eigenvalues.
- Determine the characteristic polynomial of a matrix.
- Determine whether matrices are similar.
- Determine if a given matrix is diagonalizable.
- Prove theorems involving eigenvalues and vectors.
Students must demonstrate proficiency on all CCPOs at a minimal 75 percent level to successfully complete the course. The grade will be determined using the Delaware Tech grading system:
Students should refer to the 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.
- Apply clear and effective communication skills.
- Use critical thinking to solve problems.
- Collaborate to achieve a common goal.
- Demonstrate professional and ethical conduct.
- Use information literacy for effective vocational and/or academic research.
- Apply quantitative reasoning and/or scientific inquiry to solve practical problems.
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. A listing of campus Disabilities Support Counselors and contact information can be found at the disabilities services web page or visit the campus Advising Center.