# 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.