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# LINEAR ALGEBRA

Course Description This course provides a study of linear algebra topics with emphasis on the development of
both abstract concepts and applications. Topics include vectors, systems of equations , matrices,
determinants, vector spaces, linear transformations in two or three dimensions, eigenvectors,
eigenvalues, diagonalization, and orthogonality. Upon completion, students should be able to
demonstrate both an understanding of the theoretical concepts and appropriate use of linear algebra
models to solve application problems. This course has been approved to satisfy the Comprehensive
Articulation Agreement general education core requirement in natural science/ mathematics .

Prerequisite : MAT 271

Textbook: David C. Lay, Linear Algebra and Its Applications, Third Edition,
Addison Wesley Publishing Company, 2003

Course Goal: Upon completion, students should be able to demonstrate both an
understanding of the theoretical concepts and appropriate use of linear
algebra models to solve application problems.

Course Specific Competencies: Upon successful completion of the course, the student
should be able to:
• solve linear equations in linear algebra.
• solve problems using matrix algebra.
• solve problems in vector spaces.
• evaluate eigenvalues and solve problems using eigenvectors.
• solve problems of orthogonality and least squares .
• solve problems using symmetric matrices and quadratic forms .

Content Outline
1. 1.1 Systems of Linear Equations : exercises # 7, 19 - 22, 25
2. 1.2 Row Reducation & Echelon Forms : exercises # 1 - 4, 7 - 14
3. 1.3 Vector Equations : exercises # 1 – 2, 5 - 6, 17 - 21, 25, 26
4. 1.4 The Matrix Equation Ax=B : exercises # 1 - 20, 27, 28
5. 1.5 Solution Sets of Linear Systems : exercises # 1 - 12, 29 - 34
6. 1.6 Applications: to be assigned
7. 1.7 Linear Independence : exercises # 1 - 20
8. 1.8 Linear Transformations : exercises # 1 - 6, 17 - 20
9. ** EXAMINATION 1 **
10. 2.1 Matrix Operations : exercises # 1 - 11, 17
11. 2.2 Inverse of a Matrix : exercises # 1 – 7
12. 2.3 Invertible Matrices : exercises # 1 – 10
13. 2.4 Partitioned Matrices : exercises # 1 - 10
14. 2.5 Matrix Factorizations : exercises # 1 - 12
15. 2.6 Applications: to be assigned
16. ** EXAMINATION 2 **
17. 4.1 Vector Spaces & Subspaces : exercises # 1 - 14
18. 4.2 Null & Column Spaces, and Linear Transformations : exercises # 1 - 16
19. 4.3 Linearly Independent Sets; Bases : exercises # 1 - 16
20. 4.4 Coordinate Systems : exercise # 1 - 12
21. 4.5 Dimension of a Vector Space : exercise # 1 - 18
22. 4.6 Rank : exercises # 1 - 6
23. 4.7 Change of Basis : exercises # 1 - 2, 7 - 10
24. 4.8 Applications: to be assigned
25. ** EXAMINATION 3 **
26. 5.1 Eigenvectors & Eigenvalues : exercises # 1 - 18
27. 5.2 The Characteristic Equation : exercises # 1 – 14
28. 5.3 Diagonalization : exercises # 1 – 14
29. 5.4 Eigenvectors and Linear Transformations : exercises # 1 - 2, 11 - 16
30. 5.5 Complex Eigenvalues : exercises # 1 - 14
31. ** EXAMINATION 4 **
32. 6.1 Inner Product , Length, and Orthogonality : exercises # 1 – 18
33. 6.2 Orthogonal Sets : exercises # 1 - 13
34. 6.3 Orthogonal Projections : exercises # 1 - 12
35. 6.4 Gram-Schmidt Process & QR Factorization : exercises # 1 - 14
36. 6.5 Least- Squares Problem : exercises # 1 - 12
37. 6.6 Applications: to be assigned
38. ** EXAMINATION 5 **
39. 7.1 Diagonalization of Symmetric Matrices : exercises # 1 - 12
40. 7.2 Quadratic Forms : exercises # 1 - 6
41. ** EXAMINATION 6 **

Spring Semester - 2009

 Registration: Current and Continuing Students December 1 - 5 General Registration December 8 - January 2*** Last Day to Pay Tuition and Fees January 2* * Unpaid registrations will be deleted from the computer registration system at 4:30 p.m. Late Registration January 5 - 9 Last Day to Pay Tuition and Fees for Late Registration January 9* * Unpaid registrations will be deleted from the computer registration system at 4:30 p.m. New Student Welcome January 9, 9:00 a.m. Classes Begin 12-Jan Schedule Adjustments January 12 - 13 Minimester I January 12 - March 9 Martin Luther King Jr. Day College Holiday 19-Jan Late Start Semester First Class Day 20-Jan Last Day to Drop for a Partial Refund ( Full term ) 22-Jan Professional Development - 1/2 Day 17-Feb Last Day to Apply for Spring Graduation 27-Feb Minimester II March 10 - May 12 Student Break or Inclement Weather Make-Up 13-Mar Last Day to Withdraw from a full 16-week class 7-Apr Spring College Holiday 13-Apr Student Spring Break April 13 - April 18 Last Day of Class/Examinations May 12** ** May 12 will be scheduled as a Friday make-up day Spring Graduation 15-May Total Class Days 80

** Up to three days may be made up at the end of the semester or during spring break for inclement weather.
***In person when college is open and when online registration is operational.

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