Math 272: Linear Algebra with Applications (Fall 2017)
This course concerns the core theory of linear algebra, with specific attention to applications.
Office Hours
There are many sources of help in this class; you should make use of all of them! Here are a few places you can go with your questions.
 My office hours in SMUD 510: Tuesday 2:003:30, Wednesday 1:303:00, and Friday 1:302:30 (or by appointment).
 Jen Cain (Math Fellow) office hours in SMUD 206: Tuesday and Wednesday 8pm to 9pm.
 Andrew Miller (Q Fellow) office hours in Merrill 202: see his calendar.
Homework
Problem sets will be posted here. All problem sets will be submitted online via Gradescope. Solutions will be posted after the due date. If I say that a problem set is on the “night of Wednesday,” this means that the hard deadline is 2am on the following Thursday morning.
Problems marked “selfcheck” are not to be handed in. I’ve included them as suggestions for additional practice or illustration of concepts; usually they are oddnumbered and you can check your answer in the back of the book. I will sometimes put selfcheck problems on exams, so that some problems will already be familiar.
 Course survey and Gradescope instructions. Use this to practice submitting on the Gradescope system.

Problem Set 1 (due Wednesday night, 9/13).
 §1.1: 2,12,14,16,43.
 §1.2: 10, 12, 16, 36, 38, 40, 48. [Selfcheck: 3, 2127 odd, 29, 41, 43, 49.]
 Solutions.

Problem Set 2 (due Wednesday night, 9/20).
 §1.3: 10, 12, 16, 26, 28, 38 [Selfcheck: 25, 27, 33, 37]<li>§1.4: 2, 6, 8, 22, 24, 38 [Selfcheck: 11, 19] </li><li> Solutions.</li>

Problem Set 3 (due Wednesday night, 9/27).
 §1.5: 14, 18, 26, 30 [Selfcheck: 23, 29]
 §1.8: 4, 8, 16, 20 [Selfcheck: 7, 15]
 Solutions.

Problem Set 4 (due Wednesday night, 10/11). This is not due until after the exam, and will be somewhat longer as a result.
 §2.1: 18, 20, 28, 30 [Selfcheck: 19, 25]
 §2.2: 2, 12, 18, 26, 32, 38 [Selfcheck: 25, 33, 37, 39]
 §2.3: 6, 8, 14, 24, 36, 42 [Selfcheck: 5, 9, 23, 35]
 §3.1: 2, 6, 30 [Selfcheck: 3, 27]
 Solutions

Problem Set 5 (due Wednesday night, 10/18).
 §3.2: 2, 4, 6, 18, 20, 24, 26, 30, 44, 48, 50 [Selfcheck: 9, 19, 25, 27, 45, 49]
 (Also submit Lab 3 by Wednesday night)
 Solutions

Problem Set 6 (due Wednesday night, 10/25).
 §3.3: 12, 20, 26, 36, 38, 42 [Selfcheck: 3, 13, 39]
 §3.4: 4, 14, 18, 22, 24 [Selfcheck: 5, 7, 21, 25]
 Solutions

Problem Set 7 (due Wednesday night, 11/1).
 §4.1: 22, 26, 30, 42, 44 [Selfcheck: 1, 3, 9, 13, 33]
 §4.2: 6, 16, 22, 32, 38, 40 [Selfcheck: 7, 23, 37, 39]
 (also submit Lab 4 by Wednesday night, 11/1)
 Solutions

Problem Set 8 (due Wednesday night, 11/15). This is not due until after the exam, and will be somewhat longer as a result.
 §4.3: 4, 18, 28, 30 [Selfcheck: 9, 31, 33]
 Additional problems on material from §4.3.
 §4.6: 2, 6, 8 [Selfcheck: 1,3]
 (Exam 2 material ends here)
 §4.4: 14, 20, 30, 36 [Selfcheck: 1, 7]
 §4.5: 10, 12 [Selfcheck: 17]
 Solutions

Problem Set 9 (due Wednesday night, 11/29).
 §1.6: 10, 24 [No selfcheck, but I suggest you practice computing determinants by trying some of the oddnumbered problems from 11 to 25 until you have a good feel for it]
 §5.1: 8, 16, 18, 24, 30 [Selfcheck: 13, 19, 23]
 (There will also be a lab on Monday 11/27, to be submitted by Wednesday night)
 Solutions

Problem Set 10 (due Wednesday night, 12/6).
 §5.2: 20, 34 [Selfcheck: 21, 27]
 §5.4: 2, 4 (use Mathematica or a calculator for the computations in part (b) of both problems) [Selfcheck: 3]
 Additional problems about §5.2 and §5.4.
 (Also submit Lab 6 by Wednesday night)
 Solutions

Problem Set 11 (due Wednesday night, 12/13).
 §6.1: 14, 18, 32 [Selfcheck: 29]
 §6.2: 12, 16 [Selfcheck: 13]
 Additional problems
 (Also submit Lab 7 by Wednesday night)
 Solutions
Mathematica Labs
Mathematica is available for all collegeowned computers, and is already installed in all of the public labs, e.g. in on the first floor of Seeley Mudd. If you are using a public computer, be sure to save your work to your personal user folder, or you may end up losing your work when you log out. On the other hand, you should also be sure to delete any files accidentally saved to the desktop or hard drive of these public computers to ensure that they are not visible to the next person who uses that computer.
Mathematica can also be installed on your own computer through the college’s software drive, or accessed through a remote desktop connection. The college has a limited number of Mathematica licenses, so be sure to quit Mathematica when you are finished; otherwise, you may prevent another student from being able to use it.
During the inclass labs, you may feel free to bring your own laptop and use it instead of the lab machines, as long as you have installed Mathematica.
 Introduction to Mathematica (in class 9/11; submit by email by Wednesday night 9/13).
 Linear algebra for GPS (in class 9/25; submit by email by Wednesday night 9/27).
 Based on this article by Dan Kalman.
 Linear Combinations (in class 10/16; submit by email by Wednesday night 10/18).
 Linear Transformations (in class 10/30; submit by emial by Wednesday night 11/1).
 Google PageRank (in class 11/27).
 Based on this article by Kurt Bryan and Tanya Leise.
 Least Squares (in class 12/4).
 GramSchmidt (in class 12/11).
Exams
Exams and solutions will be posted here after they are given.
Handouts and other items
 F 9/8: Example sheet and row reduction steps.
 T 9/12: Row reduction examples
 T 9/19: Left and right inverses
 W 10/18: Review of vector space concepts (Proofs of claims)
 T 10/24: Isometric drawing
 W 12/06: Quiz solutions and explicit formula for A^n example