Elementary Matrix and Linear Algebra

University credit, 12 assignments, 2 exams, $597 tuition, $60 administration fee, Prerequisites: see below. This is course U600-340.

 

Systems of linear equations, matrix equations, linear transformations. Matrix algebra, determinants, vector spaces and linear transformations. Diagonalization, eigenvalues and eigenvectors, orthogonality and least-squares. Applications of linear algebra in a variety of areas.

Prerequisites: Two semesters of college-level calculus. Before registering, please use this link to contact the Director of Mathematics.

Course Materials

• Linear Algebra and its Applications with CD-ROM, Update 3/E, David Lay. Pearson Education, Inc., 2006. Search for textbook. More information is available on David Lay's Web site, www.laylinalgebra.com
• Study Guide for Linear Algebra, also by David Lay is included in CD-ROM.
• NEW: Course Guide for Math 340 is now available at direct.mbsbooks.com/uwlearning.htm (choose "Buy Course Materials", then "Independent Learning". You will find materials listed by class number. This class is U600-340 ELEMNTRY MATRIX & LIN ALG.) or 800-325-3252.
• Student Handbook, available at learn.wisconsin.edu/il/studenthandbook/studenthandbook.pdf, or on paper by request to Learner Services, toll-free 1-877-UW-LEARN (877-895-3276)
• Additional materials will be sent by the instructor.
• Note: You may receive a registration packet which claims that you have to purchase a "course packet." You should ignore this; all materials for this course are listed above.

 

Format of Course

The course consists of 12 lessons and 2 exams. Each lesson consists of:

• A reading assignment from the text.
• Recommended problems from the text, to test your understanding.
• A written assignment from the text, to submit for grading and feedback.

Exams are mailed to a proctor selected by the student in accordance with Independent Learning's guidelines. Students may request a re-take of either exam within two weeks of receiving their graded exam back. If an exam is retaken, the higher of the two grades will be the grade of record.

Grading

Score	Letter Grade
NOTE: The grading scale was revised on Nov 13, 2003. This grading scale applies to all students who complete the course after that date.
93-100	A
90-92	AB
83-89	B
80-82	BC
73-79	C
65-72	D
0-64	F

Each lesson and each exam is graded on a 100-point scale. The final score is computed as a weighted average, with the average of the lessons counting for 60%, and the average of the exams counting 40%. The exam average must be at least 40 for a passing grade. Assuming this is the case, the average of all your work is converted to a letter grade as shown in the table.

Course Outline

• Lesson 1: Systems of linear equations
• Lesson 2: Matrix equations, solution of linear systems, applications
• Lesson 3: Independence, linear transformations
• Lesson 4: Matrix operations, inverses; invertible matrices
• Lesson 5: Matrix factorization, subspaces, dimension and rank
• Lesson 6: Determinants
• Mid-Course Exam
• Lesson 7: Vector spaces, bases, linear transformations
• Lesson 8: Coordinate systems, rank, change of basis
• Lesson 9: Eigenvalues and eigenvectors
• Lesson 10: Geometry of eigenvalues, complex eigenvalues, applications
• Lesson 11: Inner products, orthogonal projection
• Lesson 12: Gram-Schmidt process, least-squares problems
• Final Exam

Homework Assignments

Lesson 1: Systems of linear equations, vector equations

Suggested Exercises, to test your understanding. Not to turn in.
Section 1.1: #
Section 1.2: #
Section 1.3: #

Written Assignment, to turn in.
Section 1.1: #12, 14, 18, 24, 28, 34
Section 1.2: #4, 10, 12, 20, 22, 26, 30
Section 1.3: #6, 10, 14, 24, 32

Lesson 2: Matrix equations, solution of linear systems, applications

Suggested Exercises, to test your understanding. Not to turn in.
Section 1.4: #
Section 1.5: #
Section 1.6: #

Written Assignment, to turn in.
Section 1,4: #8, 12, 14, 16, 24, 26, 34
Section 1.5: #6, 10, 16, 24, 26, 40
Section 1.6: #4, 8, 12, 14

Lesson 3: Independence, linear transformations

Suggested Exercises, to test your understanding. Not to turn in.
Section 1.4: #
Section 1.5: #
Section 1.6: #

Written Assignment, to turn in.
Section 1.7: #6, 10, 12, 16, 22, 34, 36
Section 1.8: #4, 10, 12, 18, 20, 22, 26, 32
Section 1.9: #4, 8, 18, 24, 38

Lesson 4: Matrix Operations, Inverses, Invertible Matrices

Suggested Exercises, to test your understanding. Not to turn in.
Section 2.1: #1, 3, 5, 9, 11, 15, 17, 21, 27
Section 2.2: #3, 7, 9, 11, 13, 17, 21, 37
Section 2.3: #3, 5, 11, 13, 15, 17, 19, 27

Written Assignment, to turn in.
Section 2.1: #4, 6, 10, 12, 16, 18, 22, 28
Section 2.2: #6, 10, 12, 14, 18, 22, 38
Section 2.3: #12, 14, 16, 18, 20, 28

Lesson 5: Matrix Factorization, Subspaces, Dimension and Rank

Suggested Exercises, to test your understanding. Not to turn in.
Section 2.5: #5, 9
Section 2.7: #1, 3, 5, 11
Section 2.8: #1, 3, 5, 7, 9, 11, 13-18, 21, 23, 31, 33
Section 2.9: #1, 5, 7, 9, 13, 17, 19, 21, 23

Written Assignment, to turn in.
Section 2.5: #6, 10
Section 2.7: #2, 4, 6
Section 2.8: #2, 6, 8, 10, 22, 24, 32, 34
Section 2.9: #2, 6, 8, 10, 14, 18, 20, 24

Lesson 6: Determinants

Suggested Exercises, to test your understanding. Not to turn in.
Section 3.1: #1, 9, 19, 21, 23, 25, 27, 31, 33, 35, 37, 39, 41
Section 3.2: #1, 3, 5, 15, 17, 27, 29, 31, 43
Section 3.3: #17, 19, 23, Supplemental Exercises #1

Written Assignment, to turn in.
Section 3.1: #2, 10, 20, 22, 24, 26, 28, 32, 34, 36, 38, 40, 42
Section 3.2: #2, 4, 6, 16, 18, 28, 30, 32
Section 3.3: #18, 20, 24

Midterm Exam When you're getting close, you should send in the Midterm Exam Request Form (PDF). Forms can be faxed to 608-262-4096.

Lesson 7: Vector Spaces, Bases, Linear Transformations

Suggested Exercises, to test your understanding. Not to turn in.
Section 4.1: #1, 3, 4, 7, 9, 11, 13, 15, 19, 23, 25, 26
Section 4.2: #3, 9, 15, 17, 25, 27, 29, 31
Section 4.3: #3, 9, 11, 13, 15, 19, 21, 23, 29, 30, 31

Written Assignment, to turn in.
Section 4.1: #2, 10, 12, 16, 20, 24, 32
Section 4.2: #4, 10, 16, 24, 26, 28, 32
Section 4.3: #8, 10, 16, 22, 24, 32

Lesson 8: Coordinate Systems, Rank, Change of Basis

Suggested Exercises, to test your understanding. Not to turn in.
Section 4.4: #1, 3, 7, 9, 11, 13, 15, 117, 19, 23, 25
Section 4.5: #3, 7, 13, 19, 21, 23, 29
Section 4.6: #1, 3, 9, 11, 17, 19, 27, 31, 32, 33
Section 4.7: #1, 7

Written Assignment, to turn in.
Section 4.4: #4, 8, 12, 14, 16, 20, 24, 26
Section 4.5: #4, 8, 14, 20, 22, 24, 30
Section 4.6: #12, 18, 28
Section 4.7: #2, 8

Lesson 9: Eigenvalues and Eigenvectors

Suggested Exercises, to test your understanding. Not to turn in.
Section 5.1: #7, 9, 13, 17, 19, 21, 23, 25, 27, 31, 35
Section 5.2: #1, 11, 19, 21
Section 5.3: #1, 3, 5, 7, 11, 21, 23, 25, 27, 29, 31

Written Assignment, to turn in.
Section 5.1: #8, 10, 14, 18, 22(skip part c), 24, 26, 32
Section 5.2: #2, 12, 20, 22
Section 5.3: #2, 6, 8, 12, 22, 26, 30, 32

Lesson 10: Geometry of Eigenvalues, Complex Eigenvalues, Applications

Suggested Exercises, to test your understanding. Not to turn in.
Section 5.4: #1, 3, 5, 11, 15, 17, 23, 25, 31
Section 5.5: #1, 3, 5, 7, 9, 13, 15, 23
Section 5.6: #1, 5
Section 5.7: #1, 3, 5, 9, 11

Written Assignment, to turn in.
Section 5.4: #2, 4, 6, 12, 16, 18, 30
Section 5.5: #2, 6, 10, 16, 18, 24
Section 5.6: #2, 6
Section 5.7: #2, 4, 6, 10, 12

Lesson 11: Inner products, Orthogonal Projection

Suggested Exercises, to test your understanding. Not to turn in.
Section 6.1: #5, 11, 19, 21, 25, 27, 31
Section 6.2: #3, 7, 9, 11, 17, 23, 29, 31
Section 6.3: #1, 3, 7, 9, 13, 21, 23

Written Assignment, to turn in.
Section 6.1: #6, 10, 20, 22, 24, 26, 28, 30
Section 6.2: #8, 10, 12, 24, 26, 30
Section 6.3: #2, 4, 8, 14, 22, 24

Lesson 12: Gram-Schmidt Process, Least-Squares Problems

Suggested Exercises, to test your understanding. Not to turn in.
Section 6.4: #3, 5, 11, 15, 17, 19
Section 6.5: #3, 5, 7, 9, 15, 17, 19, 21
Section 6.6: #1, 3, 5, 7, 15, 16

Written Assignment, to turn in.
Section 6.4: #4, 6, 12, 16, 18, 20
Section 6.5: #4, 6, 8, 10, 16, 18, 20
Section 6.6: #2, 4, 6, 8

Final Exam When you're getting close, you should send in the Final Exam Request Form (PDF). Forms can be faxed to 608-262-4096.