Date Adopted: July 1, 1998 Date Reviewed: December 1, 1999 Date Revised: 1999, 2007, 2012 Alabama Department of Postsecondary Education Representing Alabama’s Public Two-Year College System Jefferson State Community College MTH 237 Linear Algebra I. MTH 237 Linear Algebra - 3 Semester Hours Core Area III, AMTH Al 16 TMTH (Lec 3 hrs) II. Course Descriptio n This course introduces the basic theory of linear equations and matrices, real vector spaces, bases and dimension, linear transformations and matrices, determinants, eigenvalues and eigenvectors, inner product spaces, and the diagonalization of symmetric matrices. Additional topics may include quadratic forms and the use of matrix methods to solve systems of linear differential equations. II. Prerequisite C or higher in MTH 126. IV. Textbook Elementary Linear Algebra, 5th Edition, Stanley I. Grossman, Thomson Brooks/Cole, 1994 V. Course Objectives The objective of this course is to provide an understanding of concepts, develop competent skills, and demonstrate applications in the theory of elementary linear algebra. This course seeks to further the student's introduction to the more rigorous techniques and thought processes of advanced mathematics. VI.. Course Outline of Topics A. This course shall include the following topics as a minimum: 1. Introduction to systems of linear equations 2. Gaussian elimination and Gauss-Jordan elimination 3. Applications of systems of linear equations 4. Operations with matrices 5. Properties of matrix operations 6. The inverse of a matrix 7. Elementary matrices 8. Applications of elementary matrices 9. Determinant of a matrix 10. Evaluation of a determinant using elementary operations 11. Properties of determinants 12. Applications of determinants 13. Vectors in n-space 14. Vector spaces 15. Subspaces 16. Spanning sets and linear independence 17. Basis and dimension 18. Rank of a matrix 19. Rank and systems of equations 20. Coordinates and change of basis 21. Applications of vector spaces 22. Length and dot product in n -space 23. Inner produ ct spaces 24. Orthonormal base: Gram-Schmidt process 25. Math models and least squares analysis 26. Applications of inner product spaces 27. Introduction to linear transformations 28. The kernel and range of a linear transformation 29. Matrices for linear transformations 30. Transition matrices and similarity 31. Applications of linear transformations 32. Eigenvalues and Eigenvectors 33. Diagonalization 34. Symmetric matrices and orthogonal diagonalization 35. Applications of eigenvalues and eigenvectors B. Optional topics may include the following: 1. Quadratic forms VII. Evaluation and Assessment A. College requirements: Examinations should be given by instructors periodically throughout their courses. Faculty are encouraged to give evaluative work early in the term so that students will have a clear understanding of the progress they are making. Final examinations will be given in all classes, and all students enrolled for academic credit will take the final examination. (College Handbook, section 3.7) B. Grading system as stated in the college catalog: *A - Excellent (90-100) *B - Good (80-89) *C - Average (70-79) D - Poor (60-69) F - Failure (below 60) W - Withdrawal (before last date to Withdraw) WP - Withdrawal passing (after Last date to Withdraw ) WF - Withdrawal failure (after Last date to Withdraw) I - Incomplete AU - Audit RW - Required withdrawal *Satisfactory grades C. Criteria for evaluation: 1. 2. 3. 4. Recitatio n Daily assignments Written a ssi gn ment s To receive a grade of "C" or higher, the student must obtain an average of at least 70% on written test(s) and other evaluation criteria as determined by the instructor. VIII. Class Activities A. B. C. D. E. Lecture Recitation Discussion Individual Instruction Testing IX. General Course Competencies A. The student will acquire knowledge of properties of determinants and matrices. B. The student will acquire knowledge of the properties of vector spaces and subspaces. C. The student will acquire knowledge of linear transformations. D. The student will acquire knowledge of eigenvectors and eigenvalues. X. Course Objectives Stated In Performance Terms A. The student will demonstrate knowledge of the properties of determinants and matrices by his/her ability to 1. use elementary row operations to solve systems of linear equations. 2. use Gaussian elimination to solve systems of linear equations. 3. use the inverse of a matrix to solve systems of linear equations. 4. solve systems of homogeneous equations and state the conditions under which a system will have solutions other than the trivial solution. 5. perform matrix addition, subtraction and multiplication. 6. state condition under which a matrix has an inverse and find the inverse of a matrix. 7. evaluate a determinant of any order directly and by row reduction. 8. evaluate a determinant by cofactor expansion. 9. use matrices and/or determinants to solve applied problems. B. The student will demonstrate knowledge of vector spaces and subspaces by his/her ability to 1. use the definition of a vector space to distinguish between vector spaces and other spaces. 2. compute the inner product of two vectors in a vector space and find the norm of a vector within a vector space. 3. define and find all the subspaces of a vector. 4. express any vector of a vector space as a linear combination of vectors that span the space. 5. determine a set of basis vectors for a particular subspace. 6. determine whether or not a set of vectors forms a basis for a particular space and find the dimension of the space. 7. verify that the axioms of an inner product space within a particular space hold by calculation. 8. find the length, distance, and angle in an inner product space. 9. use the Gram-Schmidt process to transform the basis of an inner product space to an orthonormal basis. XI. Attendance Students are expected to attend all classes for which they are registered. Students who are unable to attend class regularly, regardless of the reason or circumstance, should withdraw from that class before poor attendance interferes with the student’s ability to achieve the objectives required in the course. Withdrawal from class can affect eligibility for federal financial aid. XII. Statement on Discrimination/Harassment The College and the Alabama State Board of Education are committed to providing both employment and educational environments free of harassment or discrimination related to an individual’s race, color, gender, religion, national origin, age, or disability. Such harassment is a violation of State Board of Education policy. Any practice or behavior that constitutes harassment or discrimination will not be tolerated. XIII. Americans with Disabilities The Rehabilitation Act of 1973 (Section 504) and the Americans with Disabilities Act of 1990 state that qualified students with disabilities who meet the essential functions and academic requirements are entitled to reasonable accommodations. It is the student’s responsibility to provide appropriate disability documentation to the College. The ADA Accommodations office is located in FSC 300 (205-856-7731).