# Mathematics 130: Elementary Linear Algebra (Spring 2003)

Lecture: Mon-Wed-Fri 1:15pm-2:20pm (322 Cowell Hall)

Instructor: Allan Cruse
cruse@usfca.edu
Phone: (415) 422-6562
Office: 212 Harney Science Center
Office Hours: (see my homepage)

Course Assistant: Chris Cortez

Synopsis:

Numerous situations of interest in science, management and commerce can be
represented by a simple type of mathematical model called a "linear system."
Such systems are composed of one or more algebraic equations of the first
degree, involving some arbitrary number of unknown quantities (i.e., variables).

This course explores the famous Gaussian Elimination algorithm: a general
method for automatically computing all the possible solutions to any such
linear system, or for detecting that no solutions exist (as in some cases
where a system happens to include equations which are inconsistent).

The idea of a matrix (a rectangular arrangement of numbers) is fundamental
to this exploration and will be studied in detail:

• matrix manipulations (addition, subtraction, multiplication, inversion);
• elementary row and column operations, and matrix factorizations;
• the determinant for a square matrix (and what exactly it determines);
• how matrices are used to solve systems of linear equations;
• the underlying geometry of matrices, and their use as transformation operators;
• the significance of the eigenvalues and eigenvectors associated with a matrix;
• some applications to the making of optimum decisions in business management.
The course will consist of lectures, readings, discussions, quizes, and problem-sets.

Textbook:
Howard Anton, "Elementary Linear Algebra (8th Edition),"
John Wiley & Sons, Inc. (2000), ISBN 0-471-17055-0

Learning Outcomes:
• You will know how to formulate linear systems as mathematical models
• You will know how to represent any linear system by a suitable matrix
• You will be able to compute the general solution to any linear system
• You will be able to break a complicated matrix into its simpler factors
• You will be able to recognize inherent geometric properties of a matrix
• You will know how linear algebra is used for business decision-making

# Course Resources

• GAUSSIAN -- a computer program (with C++ source-code) that shows
how you can use elementary row-operations to transform a matrix into
its Reduced Row-Echelon Form (versions for Linux or for MSDOS).

# Handouts

• 0206-130-01: Course syllabus (PDF)

# Homework

• For Wed, 29 Jan 2003: Xerox Assignment Sheet #1.
• For Fri, 31 Jan 2003: Xerox Assignment Sheet #2.
• For Mon, 03 Feb 2003: Ex 1.1: #3(a,b), 4(a,c), 5(b,c), 8, 10.
• For Wed, 05 Feb 2003: Ex 1.2: #6d, 8c, 10a, 16a, 18.
• For Fri, 07 Feb 2003: Ex 1.2: #4a, 4b, 8a, 22, 24.
• For Mon, 10 Feb 2003: Ex 1.3: #2, 5f, 7c, 13b, 22c.
• For Wed, 12 Feb 2003: Ex 1.4: #7, 8, 9, 11, 13.
• For Fri, 14 Feb 2003: Ex 1.4: #14, 15, 17, 23, 29.
• For Wed, 19 Feb 2003: Ex 1.5: #2, 5a, 6b, 7c, 9.
• For Fri, 21 Feb 2003: Ex 1.5: #3, 10, 11, 15, 16b.
• For Mon, 24 Feb 2003: Ex 1.6: #4, 9, 13, 19, 20.
• For Wed, 26 Feb 2003: Ex 1.7: #6, 7, 9, 11a, 18.
• For Fri, 28 Feb 2003: No new assignment; review for Exam I.
• For Mon, 03 Mar 2003: Ex 1.7: #8, 10, 15, 19, 25.
• For Wed, 05 Mar 2003: Ex 2.1: #1, 2, 8, 12, 13.
• For Fri, 07 Mar 2003: Ex 2.1: #14, 15, 16, 17, 20.
• For Mon, 10 Mar 2003: Ex 2.2: #2, 5, 8, 12, 13.
• For Wed, 12 Mar 2003: Ex 2.3: #1, 2, 4, 5, 7.
• For Fri, 14 Mar 2003: Ex 2.3: #12, 13, 16, 17a, 18.
• (Spring Vacation: Week of March 17-21)
• For Mon, 24 Mar 2003: Ex 2.4: #1a, 1b, 3f, 4a, 4b.
• For Wed, 26 Mar 2003: Ex 2.4: #5, 10, 13, 17, 21.
• For Fri, 28 Mar 2003: Suppl. Ex. (pp. 115-116): #2, 3, 6, 7, 11.
• For Mon, 31 Mar 2003: No new assignment; review for Exam II.
• For Wed, 02 Apr 2003: Suppl. Ex. (pp. 74-75): #4, 5, 8, 15, 19.
• For Fri, 02 Apr 2003: Ex 3.1: #4, 7, 8, 9, 10.
• For Mon, 07 Apr 2003: Ex 3.2: #2c, 3d, 6a, 6b, 6c.
• For Wed, 09 Apr 2003: Ex 3.3: #3, 11, 12, 14, 22.
• For Fri, 11 Apr 2003: Ex 3.3: #4, 5, 6, 15, 23.
• For Mon, 14 Apr 2003: Ex 3.4: #2, 3, 12, 16, 18.
• For Wed, 16 Apr 2003: Ex 3.5: #4, 7, 8, 9, 10.
• (University Holiday: Fri, 18 Apr 2003: Good Friday)
• For Mon, 21 Apr 2003: Ex 3.5: #22, 29, 33, 35, 36.
• For Wed, 23 Apr 2003: No new assignment; review for Exam III.
• For Fri, 25 Apr 2003: Ex 3.5: #13, 14, 17, 21, 23.

# Announcements

• Midterm Exam 1: Friday, 28 Feb 2003
• Midterm Exam 2: Monday, 31 Mar 2003
• Midterm Exam 3: Wednesday, 23 Apr 2003
• FINAL EXAMINATION: Wednesday, 21 May 2003, 8:00am

Last updated on 04/16/2003