MATH 221-01 [2743], Fall 2013
Introduction to Linear Algebra

Course information

Course:	MATH 221-01 [2743]: Introduction to Linear Algebra
Time/Place:	TuTh 5:30pm-6:45pm, MP 103
Instructor:	Dr.  Jacob Kogan	Grader:	Luke Seppi
Office:	MP 426		MP 4th floor the math lounge
Phone:	410-455-3297
Email:	kogan at math.umbc.edu		seppi1@umbc.edu
Office hours:	Tu 3:45 PM-5:30 PM and by appointment		Th 11:30-noon

Textbook

Linear Algebra and Its Applications (fourth edition) by Lay, Addison-Wesley, 2012.

Course Description

Linear Algebra deals with systems of linear equations, their fundamental properties, and transformations of vector spaces. The basic objects of the course are vectors and matrices.

Linear algebra techniques are widely used in many areas, such as mathematics, engineering, economics, finance. They are also cornerstones for a variety of advance classes in science and engineering. The course will describe basic basic concepts and tools of linear algebra.

We will try to cover the following material: Sections 1.1-1.9, 2.1-2.3, 3.1-3.2, 4.1-4.6, 5.2-5.3, 6.1-6.4.
We may cover these topics in a different order. Depending on time we may cover more (or delete) topics.

Course Objectives

The following three topics will be emphasized:

1. the algebra of linear equations and matrices,
2. the geometry of vector spaces,
3. algorithms for solving linear equations.

• to characterize existence, uniqueness and solution sets of systems of linear equations via the row reduction algorithm,
• to perform matrix operations, including inverse and determinant computations,
• to characterize vector spaces or subspaces, and determine their dimension and matrix ranks,
• to compute eigenvectors and eigenvalues, and perform matrix diagonalization,
• concepts of orthogonality and orthogonal bases, carry out orthogonal transformations and projections.

Homework, Quizzes, Tests, and Grading

• Weekly homework will be assigned on Thursday and collected the following Thursday.
• The two lowest homework grades will be disregarded.
• Please staple your homework, and present the problems in the order assigned, if you want credit.
• No late homework will be accepted.

The final grade will be based on homework grades (20 pt), four quizzes (20 pt each), and the comprehensive final (50 pt).

Homework assignments

HW1 due Thursday 09/12/13 starts here
• Sec. 1.1, p.10: 1, 3, 12, 17, 21, 23(a)
• Sec. 1.2, p.21: 10, 12, 14, 20, 31
• Sec. 1.3, p.32: 9, 10, 12, 14, 23(c,d), 24(a,c), 26
  HW1 due Thursday 09/12/13 ends here [solutions]
  HW2 due Thursday 09/19/13 starts here
• Sec. 1.4, p.40: 2, 4, 6, 8, 9, 12, 13, 35;
  
• Sec. 1.5, p.47: 2, 8, 10, 12, 15, 18, 23(a,c,e), 35, 38
  HW2 due Thursday 09/19/13 ends here [solutions page 1] [solutions page 2]
  HW3 due Thursday, 09/26/13 starts here
• Sec. 1.7, p.60: 6, 8, 14, 18, 20, 21;
• Sec. 1.8, p.68: 2, 4, 9, 17
  HW3 due Thursday, 09/26/13 ends here [solutions]
  HW4 due Thursday, 10/03/13 starts here
• Sec. 1.8, p.68: 26, 27, 30, 32
• Sec. 1.9, p.78: 11, 15, 22, 26, 34
  HW4 due Thursday, 10/03/13 ends here [solutions]
  HW5 due Thursday, 10/10/13 starts here
• Sec. 2.1, p.100: 3, 5, 6, 12, 24, 26
• Sec. 2.2, p.109: 4, 9(a,b,c,d), 14, 16, 18, 31;
  HW5 due Thursday, 10/10/13 ends here [page 1 solutions], [page 2 solutions]
  HW6 due Thursday, 10/17/13 starts here
• Sec. 2.3, p. 115: 2, 4, 8, 11(a, d,e), 12(a,b,c), 21
• Sec. 4.1, p. 195: 16, 21, 22, 32, 33
• Sec. 4.2, p. 205: 6, 9, 14, 27, 28
  HW6 due Thursday, 10/17/13 ends here [page 1 solutions], [page 2 solutions]
  No homework due 10/24/13
  HW7 due Thursday, 10/31/13 starts here
• Sec. 4.3, p.213: 3, 8, 13, 14, 21(b,c,d), 22(a,b,e), 25, 33
• Sec. 4.5, p.229: 3, 8, 10, 14, 15, 17, 19(a,d), 20(d)
• Sec. 4.4, p.222: 3, 7
  HW7 due Thursday, 10/31/13 ends here [page 1 solutions], [page 2 solutions]
  HW8 due Thursday, 11/07/13 starts here
• Sec. 4.4, p.222: 10, 14, 22
• Sec. 4.6, p.236: 2, 3, 7, 8, 9, 11, 18(a,c);
• Sec. 3.1, p.167: 15, 33, 41, 46 (for a 3X3 matrix A)
  HW8 due Thursday, 11/07/13 ends here [page 1 solutions], [page 2 solutions],
  HW9 due Thursday, 11/14/13 starts here
• Sec. 3.2, p.175: 6, 15, 22, 35, 40
• Sec. 5.1, p.271: 7, 9, 17, 24.
  HW9 due Thursday, 11/14/13 ends here
  HW10 due Thursday, 11/21/13 starts here
• Sec. 5.2, p.279: 2, 4, 7, 8, 25
• Sec. 5.3, p.286: 6, 7, 12, 20, 21, 22(a,b)
  HW10 due Thursday, 11/21/13 ends here
• get ready for the last quiz on December 3. Topics to be covered:
  eigenvalues, eigenvectors, matrix diagonalization, orthogonal projections, orthogonal vector sets.

The Official UMBC Honors Code

By enrolling in this course, each student assumes the responsibilities of an active participant in UMBC's scholarly community in which everyone's academic work and behavior are held to the highest standards of honesty. Cheating, fabrication, plagiarism, and helping others to commit these acts are all forms of academic dishonesty, and they are wrong. Academic misconduct could result in disciplinary action that may include, but is not limited to, suspension or dismissal.

To read the full Student Academic Conduct Policy, consult the UMBC Student Handbook, the Faculty Handbook, the UMBC Integrity webpage www.umbc.edu/integrity, or the Graduate School website http://www.umbc.edu/gradschool/procedures/integrity.html.