MATH 221/0401 [4180], Fall 2007
Introduction to Linear Algebra

Course information

Course:	MATH 221/0401 [4180]: Introduction to Linear Algebra
Time/Place:	TTh 11:30am-12:45pm, MP 101
Instructor:	Dr.  Jacob Kogan	Grader:	Jason Hall
Office:	MP 427		MP 422
Phone:	410-455-3297
Email:	kogan at math.umbc.edu		h19@umbc.edu
Office hours:	Th 10:30am-11:25am and by appointment		Th 5:15 pm-6:00 pm

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 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, 09/13/07 starts here
• Sec. 1.1, p.11: 1, 7, 10, 14, 16, 21, 24(a,b,c,d);
  
• Sec. 1.2, p.25: 10, 12, 14, 20, 21(a,b,c,e), 24;
  
• Sec. 1.3, p.37: 9, 10, 12, 14, 23(c,d), 24(c,d), 26;
  HW1 due Thursday, 09/13/07 ends here
  HW2 due Thursday, 09/20/07 starts here
• Sec. 1.4, p.47: 4, 8, 9, 12, 13, 14, 22, 23(b,c,e), 36;
  
• Sec. 1.5, p.55: 2, 8, 10, 12, 15, 18, 23(a,c,e), 35, 38;
  HW2 due Thursday, 09/20/07 ends here
  HW3 due Thursday, 10/04/07 starts here
• 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
  
• 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;
  HW3 due Thursday, 10/04/07 ends here
  HW4 due Thursday, 10/11/07 starts here
• Sec. 2.1, p.116: 2, 4, 8, 10, 16(c,d,e), 20;
  
• Sec. 2.2, p.126: 4, 8, 9(b,c,d), 14, 16, 18, 31;
  HW4 due Thursday, 10/11/07 ends here
  HW5 due Thursday, 10/25/07 starts here
• Sec. 2.3, p.132: 2, 4, 8, 11(a, d,e), 12(a,b,c), 22 where H is a square matrix;
  
• Sec. 4.1, p.223: 5, 12, 13, 16, 18, 24(b,c,d); see Example 8 for 24(d).
  HW5 due Thursday, 10/25/07 ends here
  HW6 due Thursday, 11/01/07 starts here
• Sec. 4.2, p.234: 6, 9, 14, 17, 18, 24, 25(a,b), 26(a,b,c);
  
• Sec. 4.3, p.243: 3, 8, 13, 14, 21(b,c), 22(a,b,e);
  HW6 due Thursday, 11/01/07 ends here
  HW7 due Thursday, 11/15/07 starts here
• 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);
  HW7 due Thursday, 11/15/07 ends here
  HW8 due Thursday, 11/29/07 starts here
• Sec. 4.6, p.269: 2, 3 (skip the questions on row spaces in 2 and 3), 7, 8, 9, 11, 18(a,c);
  
• Sec. 3.1, p.190: 2, 9, 12, 19, 20, 21, 29, 33, 34, 36;
  
• Sec. 3.2, p.199: 6, 15, 17, 19, 22, 25, 27(a,c,d);
  HW8 due Thursday, 11/29/07 ends here
• Sec. 5.1, p.309: 5, 8, 12, 13, 15, 21(a, b, c), 22(d,e);
  
• Sec. 5.2, p.317: 2, 4, 11, 12, 16 (find the eigenvalues only without considering the multiplicities);
  
• Sec. 5.3, p.325: 6, 7, 12, 15, 20, 21(a,d), 22(a,b), 23;
  
• Sec. 6.1, p.382: 2, 7, 10, 14, 16, 17, 20(a, b);
  
• Sec. 6.2, p.392: 3, 8, 12, 16, 23(a, e), 24(a, b);
  
• Sec. 6.3, p.400: 4, 5, 8, 9, 11, 12, 21 (a, b, c, d);
  
• Sec. 6.4, p.407: 5, 11; (find the solution on p. A50)
  

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