Mathematics 130: Elementary Linear Algebra (Fall 2004)

Lecture: Mon-Wed-Fri 1:30pm-2:35pm (Room HRN-509)

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

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:

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)
• Supplementary notes on Lesson 1 (.pdf format)
• Supplementary notes on Lesson 2 (.pdf format)

Homework

• For Mon, 30 Aug 2004: Assignment Sheet #1 (.pdf)
• For Wed, 01 Sep 2004: Assignment Sheet #2 (.pdf)
• For Fri, 03 Sep 2004: Ex 1.1: #3(a,b), 4(a,c), 5(b,c), 8, 10.
• For Wed, 08 Sep 2004: Ex 1.2: #6d, 8c, 10a, 16a, 18.
• For Fri, 10 Sep 2004: Ex 1.2: #4a, 4b, 8a, 22, 24.
• For Mon, 13 Sep 2004: Ex 1.3: #2, 5f, 7c, 13b, 22c.
• For Wed, 15 Sep 2004: Ex 1.4: #7, 8, 9, 11, 13.
• For Fri, 17 Sep 2004: Ex 1.4: #14, 15, 17, 23, 29.
• For Mon, 20 Sep 2004: Ex 1.5: #2, 5a, 6b, 7c, 9.
• For Wed, 22 Sep 2004: Ex 1.5: #3, 10, 11, 15, 16b.
• For Fri, 24 Sep 2004: Ex 1.6: #4, 9, 13, 19, 20.
• For Mon, 27 Sep 2004: Ex 1.7: #6, 7, 9, 11a, 18.
• For Wed, 29 Sep 2004: No new assignment; review for Exam I.
• For Fri, 01 Oct 2004: Ex 1.7: #8, 10, 15, 19, 25.
• For Mon, 04 Oct 2004: Ex 2.1: #1, 2, 8, 12, 13.
• For Wed, 06 Oct 2004: Ex 2.1: #14, 15, 16, 17, 20.
• For Fri, 08 Oct 2004: Ex 2.2: #2, 5, 8, 12, 13.
• For Mon, 11 Oct 2004: Ex 2.3: #1, 2, 4, 5, 7.
• For Wed, 13 Oct 2004: Ex 2.3: #12, 13, 16, 17a, 18.
• For Fri, 15 Oct 2004: Ex 2.4: #1a, 1b, 3f, 4a, 4b.
• For Mon, 18 Oct 2004: Ex 2.4: #5, 10, 13, 17, 21.
• For Wed, 20 Oct 2004: Suppl. Ex. (pp. 115-116): #2, 3, 6, 7, 11.
• For Fri, 22 Oct 2004: No new assignment; review for Exam II.
• For Mon, 25 Oct 2003: Suppl. Ex. (pp. 74-75): #4, 5, 8, 15, 19.
• For Wed, 27 Oct 2004: Ex 3.1: #4, 7, 8, 9, 10.
• For Fri, 29 Oct 2004: Ex 3.2: #2c, 3d, 6a, 6b, 6c.
• For Mon, 01 Nov 2004: Ex 3.3: #3, 11, 12, 14, 22.
• For Wed, 03 Nov 2004: Ex 3.3: #4, 5, 6, 15, 23.
• For Fri, 05 Nov 2004: Ex 3.4: #2, 3, 12, 16, 18.
• For Mon, 08 Nov 2004: Ex 3.5: #4, 7, 8, 9, 10.
• For Wed, 10 Nov 2004: Ex 3.5: #22, 29, 33, 35, 36.
• For Fri, 12 Nov 2004: Ex 3.5: #13, 14, 17, 21, 23.
• For Mon, 15 Nov 2004: Xerox assignment sheet #3 (setup).
• For Wed, 17 Nov 2004: Xerox assignment sheet #4.
• For Fri, 19 Nov 2004: Xerox assignment sheet #3 (solve).
• For Mon, 22 Nov 2004: No new assignment; review for Exam III.
• For Wed, 24 Nov 2004: Ex 4.1: #2, 3, 15, 16, 20.
• For Mon, 29 Nov 2004: Ex 4.2: #2(a,b,c,d), 4(a,b,c,d), 9(b), 13(a).
• For Wed, 01 Dec 2004: Ex 4.2: #6(a,b,c,d), 7(a,b), 12(a), 15(a,b,c).
• For Fri, 03 Dec 2004: Ex 4.3: #2(a,b,c,d), 3, 4, 18(a,c), 19(b,d).
• For Mon, 06 Dec 2004: Ex 4.3: #15, 16, 21, 22, 23.
• For Wed, 08 Dec 2004: No new assignment; review for Final Exam.

Announcements

• Midterm Exam 1: Wednesday, 29 September 2004
• Midterm Exam 2: Friday, 22 October 2004
• Midterm Exam 3: Monday, 22 November 2004
• FINAL EXAMINATION: Thursday, 16 Dec 2004, NOON

Last updated on 12/03/2004