Linear Algebra and Probability, Spring 2018 
1  Mon, 22 Jan  Download the Course Syllabus.
Homework: Read pp. 3—11, and do Exercises #1—5, 7. Visit last year's website for sample quizzes, exams, and much, much more! 
2  Wed, 24 Jan 
Homework: Finish reading Section 2.0 (but skip all the trigonometric derivations on pp. 14—16). Do problems 9—10, 12—16, and 18. Homework answers: 1. (a) $x=2.$ (b) $x=0, 3.$ (c) $x=3,3.$ (d) all real numnbers. 2. False (consider a $0$ scalar multiple). 3. True (no difficulties with nonzero scalar multiples). 4. $x=1+2t, y=4+2t$ (other answers are possible). 5. $x=32t, y=1+t$ (other answers are possible). 
3  Fri, 26 Jan 
Read Section 2.1. Do p. 25, Exercises #1(a)—(c), 2, 3(a)—(c), 4, 5. There will be a Homework Quiz next Wednesday! Answers to selected homework Exercises (starting on p. 13): 10. $\left(\begin{matrix}2\\5\end{matrix}\right).$ 12. $\left(\begin{matrix}1\\2\end{matrix}\right).$ 13. $45^\circ.$ 14. $135^\circ.$ 15. $\left(\begin{matrix}3/10\\1/10\end{matrix}\right).$ 16. $\left(\begin{matrix}1\\2\end{matrix}\right).$ 18. $\sqrt5.$ 
4  Mon, 29 Jan 
Nick's office hours tonight are from 5:00—7:00 in Room 315 in the library. Answers to yesterday's homework: 1(a). $x'=x,\quad y'=0.$ 1(b). $x'=0,\quad y'=y.$ 1(c). $x'=\dfrac{xy}2,\quad y'=\dfrac{yx}2.$ 2. $a'=\dfrac{4a+10b}{29},\quad b'=\dfrac{10a+25b}{29}.$ 3(a). $x'=x,\quad y'=y.$ 3(b). $x'=x,\quad y'=y.$ 3(c). $x'=y,\quad y'=x.$ 4. $a'=\dfrac{21a+20b}{29},\quad b'=\dfrac{20a+21b}{29}.$ 5a. $\left[\begin{matrix}0&1\\1&0\end{matrix}\right].$ 5b. $\left[\begin{matrix}1&0\\0&1\end{matrix}\right].$ 5c. $\left[\begin{matrix}1&0\\0&1\end{matrix}\right].$ Download a useful summary of linear and affine transformations. Today's homework:

5  Wed, 31 Jan 
Answers to yesterday's HW (questions involving formulas): 1. $f\left(\begin{matrix}x\\ y\end{matrix}\right)=\left[\begin{matrix}2&0\\0&1\end{matrix}\right]\left(\begin{matrix}x\\ y\end{matrix}\right)+\left(\begin{matrix}2\\ 1\end{matrix}\right).$ 2. $f\left(\begin{matrix}x\\ y\end{matrix}\right)=\left[\begin{matrix}1&0\\0&1\end{matrix}\right]\left(\begin{matrix}x\\ y\end{matrix}\right)+\left(\begin{matrix}1\\ 0\end{matrix}\right).$ 6. $f\circ g\left(\begin{matrix}x\\ y\end{matrix}\right)=\left(\begin{matrix}y\\ x\end{matrix}\right)$ and $g\circ f\left(\begin{matrix}x\\ y\end{matrix}\right)=\left(\begin{matrix}y\\ x\end{matrix}\right).$ Here is the fractal we looked at in class today. Today's homework:

6  Fri, 2 Feb 
Answers to yesterday's homework: 1. $f\left(\begin{matrix}x\\ y\end{matrix}\right)=\left[\begin{matrix}1&0\\0&1\end{matrix}\right]\left(\begin{matrix}x\\ y\end{matrix}\right)+\left(\begin{matrix}3\\ 2\end{matrix}\right).$ 2. $\left[\begin{matrix}0&3\\2&0\end{matrix}\right].$ 3. $f\left(\begin{matrix}x\\ y\end{matrix}\right)=\left[\begin{matrix}1&0\\0&1\end{matrix}\right]\left(\begin{matrix}x\\ y\end{matrix}\right)+\left(\begin{matrix}1\\ 0\end{matrix}\right).$ Homework: Section 2.3: Read up to p. 44; #3, 4, 8, 9; Section 2.5: Read all; #1, 2(i)(ii). Also, what affine transformations would you need to create this fractal? Here is some help on using Processing for the first time. Download the Processing code to visualize linear transformations. You will need to copy and paste into a new sketch. Download the Processing code to create fractals using iterated function systems. 
7  Mon, 5 Feb 
Nick will be in Room 315 in the library from 5:00—7:00 tonight. Prof. Tom Banchoff will be speaking at 3:30 in Cowell 107 (and there is food in the Getty Lounge (where the fireplace is in Lo Schiavo) starting at 3:00). Partial solutions to HW: Section 2.3. #3. $PR=\left[\begin{matrix}0&1\\0&0\end{matrix}\right].$ $RP=\left[\begin{matrix}0&0\\1&0\end{matrix}\right].$ #4(a). $\left[\begin{matrix}1&0\\0&0\end{matrix}\right].$ (b). $\left[\begin{matrix}0&0\\0&0\end{matrix}\right].$ (c). $\left[\begin{matrix}19&22\\43&50\end{matrix}\right].$ #8. See 4(b). Partial solutions to HW: Section 2.5. #1. $\left[\begin{matrix}1&11\\3&23\end{matrix}\right].$ Homework problems (assume the cube has as vertices all combinations of $(\pm1,\pm1,\pm1)$ as in class today):

8  Wed, 7 Feb 
Write out all 24 matrices describing the direct symmetries of the cube. Annotate each one with an appropriate picture of a die! Partial homework answers: 1. $\left[\begin{matrix}0&1&0\cr 0&0&1\cr 1&0&0\end{matrix}\right],$ $\left[\begin{matrix}0&0&1\cr 1&0&0\cr 0&1&0\end{matrix}\right],$ and $\left[\begin{matrix}1&0&0\cr 0&1&0\cr 0&0&1\end{matrix}\right].$ 2. $\left[\begin{matrix}0&0&1\cr 0&1&0\cr 1&0&0\end{matrix}\right].$ 
9  Fri, 9 Feb 
Download the book chapter about the hypercube. Get caught up with homework! 
10  Mon, 12 Feb 
Nick's office hours will be in Room 314 in the Library this evening from 5:00—7:00. Homework:

11  Wed, 14 Feb 
Homework answers:
Download solutions to Homework Quiz 1B. In case the first quiz didn't go so well, you can practice with a copy of the version you didn't take. Download a blank copy of Homework Quiz 1A or Homework Quiz 1B. Here are the homework problems on the cross product due Friday. Your assignment is #9, 11, 29, 31, 35, 44, 46, and 47. Here is a summary of the the direct symmetries of the cube. Here is another fractal to practice writing affine transformations which describe its selfsimilarity. 
12  Fri, 16 Feb 

13  Wed, 21 Feb 
Nick's office hours will be in Room 315 in the Library this evening from 5:00—7:00. Download solutions to Homework Quiz 2. Just study for Friday's Midterm! No notes, no calculators, and be on time. NO EXTRA TIME will be given if you arrive late! 