**SSEA Math Module 2012 - 51 Track**

**Instructor:** Henry Adams
**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.