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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 GramSchmidt 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  12Jan 
Schedule Adjustments  January 12  13 
Minimester I  January 12  March 9 
Martin Luther King Jr. Day College Holiday  19Jan 
Late Start Semester First Class Day  20Jan 
Last Day to Drop for a Partial Refund ( Full term )  22Jan 
Professional Development  1/2 Day  17Feb 
Last Day to Apply for Spring Graduation  27Feb 
Minimester II  March 10  May 12 
Student Break or Inclement Weather MakeUp  13Mar 
Last Day to Withdraw from a full 16week class  7Apr 
Spring College Holiday  13Apr 
Student Spring Break  April 13  April 18 
Last Day of Class/Examinations  May 12** 
** May 12 will be scheduled as a Friday makeup day  
Spring Graduation  15May 
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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