SSEA Math Module - Summer 2012 - 51 track

SSEA Math Module 2012 - 51 Track

Email: henry dot adams at colostate dot edu

Teaching Assistants: Anthony Alvarado, Fidel Hernandez, and Shaheen Jeeawoody
Emails: aalvara1 at stanford dot edu, fidelh at stanford dot edu, and shaheenj at stanford dot edu

Textbook: Linear Algebra by Levandosky.
This is the textbook for the linear algebra portion of Math 51 during the school year.

Schedule: In the table below, lectures are in red and sections are in blue. Discussion problems will be listed for each section.

 Week 1 Aug 6 Diagnostic Test Aug 7 Section Review diagnostic test Aug 8 Vectors Linear Combinations and Span Equations of Lines §1-2 Aug 9 Section §1: #3, 5, 7, 9, 11 §2: #1, 11, 12, 13 Aug 10 Equations of Planes Linear Independence §2-3 Week 2 Aug 13 Section §2: #3, 5, 9, 15 §3: #1, 3, 5, 9, 11, 13 Aug 14 Systems of Linear Equations Reduced Row Echelon Form of a Matrix §5-6 Homework 1 due Aug 15 Section §6: #1, 3, 5, 9, 11, 13 Aug 16 Matrix-Vector Products The Null Space of a Matrix §7-8 Aug 17 Section §7: #1, 3 §8: #1, 9, 12, 15, 22, 23, 25 Week 3 Aug 20 The Column Space of a Matrix Subspaces §9-10 Homework 2 due Aug 21 Section §9: #1, 6, 7, 11, 14, 16 §10: #11, 16, 21 Aug 22 Subspaces: Bases and Dimension Bases for Column Space and Null Space The Rank-Nullity Theorem §11-12 Aug 23 Section §11: #1, 5, 8, 13 §12: #1, 5, 13 Aug 24 Linear Transformations The Matrix of a Linear Transformation §13-14 Homework 3 due Week 4 Aug 27 Section §13: #1, 3, 11, 12, 17 (T is a linear transformation in #17) §14: #2, 7, 10 Aug 28 More Examples of Linear Transformations Composition and Matrix Multiplication §14-15 Aug 29 Section §14: #5, 12, 14 §15: #1(b, c, f, g, h), 3 Aug 30 Final Exam Homework 4 due

Homework: Homework is due every four days, in lecture. The challenge problems are optional, and you should only attempt them after you finish the homework. Please submit the challenge problems on a separate page, and please do not worry if you cannot solve the challenge problems!

Homework 1, due Tuesday Aug 14 in lecture.
§1: #4, 8, 10
§2: #2, 4, 8, 10, 14, 16
§3: #2, 4, 6, 8, 10, 12
Selected solutions.
Challenge problems 1.

Homework 2, due Monday Aug 20 in lecture.
§6: #4, 6, 8, 10, 14
§7: #2, 4
§8: #4, 8, 11, 13, 14, 18, 20
Challenge problems 2.

Homework 3, due Friday Aug 24 in lecture.
§8: #24
§9: #2, 8, 12
§10: #15, 17, 20
§11: #2, 6, 11, 12
§12: #2, 9, 12
Challenge problems 3.

Homework 4, due Thursday Aug 30 at beginning of final exam.
§13: #2, 6, 13, 16, 22
§14: #1, 3, 8, 11 [#6 has been removed]
§15: #1(a, d, e, i), 4 [#6 has been removed]
Challenge problems 4.

Practice Final Exam:
Here is a practice final exam, and here are solutions.

Final Exam:
Here is the final exam and here are solutions. This test was not short or easy. The mean was 74.5, the median was 75, and the standard deviation was 12.9. I predict that grades between 79 and 100 would be on pace for an A during the term, that grades between 60 and 78 would be on pace for a B, and that grades 59 or below would be on pace for a C.

Notes:
Notes on rank, nullity, existence, and uniqueness, August 22.