MATH 221-05 [3576], Spring 2010
Introduction to Linear Algebra

Course information

Course:	MATH 221-05 [3576]: Introduction to Linear Algebra
Time/Place:	MoWe 5:30pm-6:45pm, MP 103
Instructor:	Dr.  Jacob Kogan	Grader:	Chandan Kawad
Office:	MP 427
Phone:	410-455-3297
Email:	kogan at math.umbc.edu		ckawad1@umbc.edu
Office hours:	MoWe 6:45 PM-7:30 PM and by appointment

Textbook

Linear Algebra and Its Applications (third edition) by Lay, Addison-Wesley, 2003. Text webpage is http://www.laylinalgebra.com.

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 Wednesday and collected the following Wednesday.
• 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 Wednesday, 02/03/10 starts here
• Sec. 1.1, p.11: 1, 3, 12, 17 [solutions]
  HW1 due Wednesday, 02/03/10 ends here
  HW2 due Wednesday, 02/17/10 starts here
• Sec. 1.1, p.11: 16, 21, 23(a,b,c)
  
• Sec. 1.2, p.25: 10, 12, 14, 20, 31 [solutions]
  HW2 due Wednesday, 02/17/10 ends here
  HW3 due Wednesday, 02/24/10 starts here
• Sec. 1.3, p.37: 9, 10, 12, 14, 23(c,d), 24(c,d), 26;
  
• Sec. 1.4, p.47: 2, 4, 6, 8, 9, 12, 13;
  HW3 due Wednesday, 02/24/10 ends here [solutions]
  HW4 due Wednesday, 03/03/10 starts here
• Sec. 1.4, p.47: 14, 22, 23(b,c,e), 34, 36;
  
• Sec. 1.7, p.71: 6, 8, 14, 18, 20, 21; (hint to 21(d): see Example 4 of Sec. 1.7.), 33, 34, 37
  HW4 due Wednesday, 03/03/10 ends here [solutions]
  HW5 due Wednesday, 03/10/10 starts here
• Sec. 1.5, p.55: 2, 8, 10, 12, 15, 18, 23(a,c,e), 35, 38;
  
• Sec. 2.2, p.126: 4, 9(b,c,d), 14, 16, 18, 31;
  HW5 due Wednesday, 03/10/10 ends here [solutions]
  No homework for the weeks March 10, 2010-March 24, 2010
  enjoy the break!
  HW6 due Wednesday, 03/31/10 starts here [solutions]
• Sec. 1.8, p.79: 2, 4, 9, 17, 19, 21(b,c), 25, 29, 36;
  
• Sec. 1.9, p.90: 8, 13, 22, 23, 24, 26, 32, 35;
  HW6 due Wednesday, 03/31/10 ends here
  HW7 due Wednesday, 04/07/10 starts here [solutions]
• Sec. 4.1, p.223: 5, 12, 13, 16, 18, 24(b,c,d); see Example 8 for 24(d).
  HW7 due Wednesday, 04/07/10 ends here
  HW8 due Wednesday, 04/14/10 starts here [solutions]
• Sec. 4.2, p.234: 6, 9, 14, 17(a), 18(a), 25(a,b), 26(a,b), 27, 28;
  HW8 due Wednesday, 04/14/10 ends here
  HW9 due Wednesday, 04/21/10 starts here [solutions]
• Sec. 4.2, p.234: 17(b), 18(b), 24, 26(c);
  
• Sec. 4.3, p.243: 3, 8, 13, 14, 21(b,c), 22(a,b,e);
  HW9 due Wednesday, 04/21/10 ends here
  HW10 due Wednesday, 04/28/10 starts here [solutions]
• Sec. 4.4, p.253: 3, 7, 10, 14, 22;
  
• Sec. 4.5, p.260: 3, 8, 10, 14, 15, 17, 19(a,d), 20(a,b,d);
  HW10 due Wednesday, 04/28/10 ends here
  No homework for the week April 29, 2010-May 5, 2010
  get ready for quiz 4!
  List od suggested practice problems:
• Sec. 4.6, p.269: 2, 3, 7, 8, 9, 11, 18(a,c);
• Sec. 5.2, p.317: 2, 4, 7, 8, 25

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