"What is written without effort is in general read without pleasure."  
                                                   Samuel Johnson (1709-1784)

Homework Due Date/Reading	Problems to Hand In	Other Recommended Problems (not to hand in)	Handouts & Solutions
Read Section 6.6 Read 7.1 (We covered most of this in class in the final lecture. You can skip the couple of paragraphs about the spectral decomposition, although we'd certainly have talked about that if we'd had time.) We also introduced the material in 7.2 -- it would be good to read 7.2 but it won't be on the final.  .	No more problems to hand in.  But you should do the recommended problems in preparation for the final exam.	Sec 6.6:  7a, 8a, 9, 10a Sec 7.1:  3,5,7,9,19,25(a,b,c),26
	OLDER STUFF               BELOW
Quiz in class Friday, 12/5 HW 12, due in class  Friday, 12/5.  This is the last "hand-in homework.  I will suggest some addition problems to practice with the material beyond what's on HW 12. Section 6.3 was finished in class Monday, 11/24.  Please be "up-to-date" on that after reak. Read Sec 6.4 (you can skip the last section on QR factorization) Read Sec 6.5 (you can skip Theorem 15, p. 414 ))	Always include enough or explanation or calculation in every homework solution so the reader can understand how you got your answer. Sec 6.2: 10,14, 20, 28 Sec 6.3: 10, 12, 20, 24 Sec 6.4: 4,10 Sec 6.5: 4,6,10,14 Sec 6.6: 4	Sec 6.2:  9,13,15, 23,24 Sec 6.3:  9,11,19, 21,22 Sec 6.4:  17,18 Sec 6.5:  3,5,9,13,17,18	Notes on the Gram Schmidt Process Quiz 5 Solutions Optional Exam 3: Solutions Homework 12 Solutions
HW 11 due in class on Friday, 11/24 Read Sec 5.5 Read Sec 5.6.  You can skip the couple of paragraphs about "Change of Variable" if you like. Skip Sec 5.7 - 5.8 Read Sec 6.1-6.3	Always include enough or explanation or calculation in every homework solution so the reader can understand how you got your answer. Sec 5.5:  6,10,12,18 Sec 5.6:  2, 4, 6  (find a nonzero value of p) Sec 6.1:  4,6,12,18,24,28	Sec 5.5:  5,9,11,15 Sec 5.6:  5 Sec 6.1:  5,7,19,20	Simple example illustrating the ideas of Section 5.5 Proofs of the results in Section 5.5 Another Example with a 2x2 Real Matrix with Complex Eigenvalues The Spotted Owls Homework 11 Solutions
Quiz in Class on Friday, 11/14 covering 5.1-5.3 Read Sec. 5.3-5.4-5.5 Read Appendix B  (pp. A3-A8) with as much care as needed for a review of complex numbers) HW 10 due in class Friday, 11/14 -- problems to be posted soon.	Always include enough or explanation or calculation in every homework solution so the reader can understand how you got your answer. Sec 5.3: 4,6,10,14,24,26 (for # 14): notice that, to save you time, the eigenvalues are given in the text in a paragraph immediately following Exercise 6) Sec 5.4:  4,10,14,22, 26 (look back at #25 for the definition of "trace."  You may use anything stated in #25 if it's helpful.)	Sec 5.3:  3,5,13,21,22,23,25 Sec 5.4:  3,9,13,23	Relation among dimension of eigenspaces, multiplicity of eigenvalues and diagonalization Theorem 7, p. 324: Error in Textbook Matrices for Linear Transformations: Examples Quiz 4 Solutions Homework 10 Solutions
Exam 2 in class Friday, November 7 (see information above) Because of the test, HW 9 will be due in class on Monday, 11/10 Read 5.1 - 5.2 (a lot in 5.2 is material we already covered on determinants -- but a good brush-up review of the basics)	Always include enough or explanation or calculation in every homework solution so the reader can understand how you got your answer. Sec 4.6:  4,8,10,16,22 Do this Supplementary Problem on Markov Processes Sec 5.1:  14,18,24,26, Sec 5.2:  8,14,18	Sec 4.6: 3,6,9,11,17,18 Sec 5.1: 5,7,13,17,21,22,27 Sec 5.2:  7,13	Examples of Calculations for Eigenvalues and Eigenspaces, Diagonalization Another Diagonalization Example Theorems about linearly independent eigenvectors Homework 9 Solutions Exam 2 Solutions Math 309 Scores, including Exam 2
Read Sec 4.5- 4.6  Be sure you've read all the supplementary handouts from last week. Skip Sections 4.7-4.8 Read 4.9 and related handout on Markov Processes HW 8, due in class on Friday, October 31 Exam 2 in class Friday of NEXT week (November 7)	Always include enough or explanation or calculation in every homework solution so the reader can understand how you got your answer. Sec 4.4: 12,20,30 Sec 4.5:  6,8,12,22 Do the Supplementary Problems here on Diagonalization Do the Supplementary Problem here on Rotation of AxesS	Sec 4.4: 15,16,31 Sec 4.5:  5,15,19,20,29,30	Invertible Matrix Theorem, Updated Section 4.6 Introduction to Markov Processes Homework 8 Solutions
Items in this row cover MW of Fall Break Week + the week after Fall Break.  Because of Fall Break, HW 7 is due Friday, October 24--so it'll be a bit onger than usual. Friday, October 24 is also a QUIZ day. Read 4.1 - 4.4 and handout notes on diagonalization	Always include enough or explanation or calculation in every homework solution so the reader can understand how you got your answer. Sec 4.1: 2,6,16,18,22 Sec 4.2: 4,10,12, 16,18,24,28,32 Sec 4.3: 8,14,16,20,26, 32 (#32 should also assume that "T is linear") Sec 4.4: 4,8,14	Sec 4.1: 5,17, 23,24,31 Sec 4.2: 5,23,25,26 Sec 4.3: 1,3,5,11,21,22,29,30,33 Sec 4.4: 3,7,13	Class handout about Nul A and Col A Two Examples about Bases Example: Basis for Col A and Nul A Example: A Nonstandard basis for the plane Example: The isomorphism between P3 and R4 Introduction to Diagonalization Supplementary Example: Rotation of Axes Homework 7 Solutions
HW 6  Due in class Friday, October 10 Read Sec 3.2. In Sec 3.3, skip up to "Determinants as Area or Volume" and read from there to the end of the section. You might want to just quickly scan the earlier material, and the "Numerical Note" about the skipped material on Cramer's Rule. Read Section 4.1	Always include enough or explanation or calculation in every homework solution so the reader can understand how you got your answer. Sec 3.1: 18 (read paragraph preceding exercise) Sec 3.2: 8,12,16,18,20,24, 34,36,40(c,d,e) Sec 3.3:  Do the two problems on this supplementary sheet and then also 30,32	Sec 3.1: 15,39,40 Sec 3.2:  7,11,21,27,28,31 Sec 3.3:  21,23,31	Exam 1 Solutions Math 309 Scores, including Exam 1 Homework 6 Solutions
HW 5 Due in class Friday, October 3 Skip Sec. 2.5, 2.7 (you might be interested in a quick read of 2.7 if you're in computer science; and perhaps 2.5 if you're in EE --although in 2.5, the algebra leading up to the example it a bit harder to read.) Read Sec 2.6 (and Notes on 2.6); read Sec 3.1 EXAM 1: IN CLASS MONDAY, OCT. 6 NO QUIZ THIS FRIDAY	Always include enough or explanation or calculation in every homework solution so the reader can understand how you got your answer. Sec 2.3 (Note the opening sentence at the start of these exercises :  "Unless otherwise stated, assume...") :   6,16, 22,24,26,34,38 Sec 2.4:  4,6 (assume all blocks are square)               10 ("find X,Y,Z"  means "find X,Y,Z in terms of A,B,C") Sec 2.6:  2,6,8 Sec 3.1:  2, 8, 20, 22	Sec 2.3: 3,7,11,12,13,23,29 Sec 2.4: 1,3,7 Sec 2.6: 3 Sec 3.1: 1,7,19,21	Notes on Section 2.6: Leontief Open Economy Model Leontief Example with Real Data Elementary Matrices, EROs, and Determinants Homework 5 Solutions
HW 4 Due in class Friday, September 26 Complete reading Sec. 2.1-2.3 Read Sec. 2.4 (in this one section, I'm mainly interested in the mechanical stuff)	Always include enough or explanation or calculation in every homework solution so the reader can understand how you got your answer. Sec 1.9:  18, 28, 30 Sec 1.10:  10 Sec 2.1:  6,12,18,20,22,28 Sec 2.2:  6, 8,16,18,20,               22,24,30,32,38	Sec. 1.9:  15,23,24,35 Sec 1.10:  9 Sec 2.1:  5, 9,11,15,16 Sec 2.2:  9,10,13,15,31,33	Linear Difference Equation Example (Speedy Car Rental) Matrix Multiplication Examples The Transpose Theorem Effect of Elementary Matrices The Invertible Matrix Theorem (my presentation chart) Homework 4 Solutions
HW 3 Due in class Friday, September 19 Read Sec 1.7-1.8-1.9 Read Example of Difference Equations in Sec 1.10. Start reading Sec 2.1 Quiz in class, Friday, September 19.	Always include enough detail in every homework solution so the reader can understand how you got your answer. Sec 1.5: 14,16,18,22,28,36 Sec 1.7: 12,24,28,38 Sec 1.8:  6,12,18,24,32,34 Sec 1.9:  4,6,8,10,12	Sec 1.5:  13,17,19,23,24, 26,31,37 Sec 1.7:  13,17,19,21,22,25 Sec 1.8:  5,9,13,16,21,22,27,31 Sec 1.9:  3,5,11	Summary Sheet on Linear Transformations and Matrices for Sections 1.8-1.9 Quiz 2 Solutions Homework 3 Solutions
HW 2: Due in class Friday, September 12 Read Sec. 1.4 Read Sec. 1.5 Read Sec. 1.6 Start reading Sec 1.7	Always include enough detail in every homework solution so the reader can understand how you got your answer. Sec 1.3:  10, 16, 18, 26 Sec 1.6:  14 Sec 1.4:  6,16,20,22,28,34 Sec 1.5:  4,6,12	Sec 1.3: 23, 24 Sec 1.6: 13 Sec 1.4:  7,13,23,24,26,35 Sec 1.5:  3,5	Extra Example (Wednesday lecture) Similar to class example, but there are some comments near the end that are important to read. Homework 2 Solutions
Hand-in Homework 1 due in class Friday, September 5 Be sure to read How to Study Linear Algebra at this link OR in your Study Guide. Read Note to Students on pp. xxxv-xxxvi Be sure to read the Introductory Example (about Leontief) at the start of Chapter 1. Read Sections 1.1-1.3 Read Section 1.6 Note: Quiz in class Friday, Sept. 5	Sec 1.1:  16,  20, 28, 34 (this requires doing 33 first: check answer to 33 in the back of the text before doing 34) Sec 1.2: 10, 14, 16(b),18, 30 (refer back to #29) Sec 1.3: 8, 12, 14	Sec 1.1:  1,5,7,13,15, 23,24,27,25,33 Note: nearly every section contains  exercises (like #23, 24) with a list of true/false questions.  You should always do those, even if I don't mention the problem here. Sec 1.2:  3,13,15, 19, 21, 22, 23, 27, 29, 31 Sec 1.3:  5,7, 11,13	Example: Closed Exchange Economy Practice Sheet Solutions for Quiz 1 Homework 1 Solutions

Linear Algebra and Its Applications, by David Lay.  This text is very well-written and is a must-read as the course moves along. 

A copy of the author's Study Guide should be bundled with your textbook at the Campus Bookstore. The Study Guide is a very valuable resource.  I recommend that you consistently use it as you work your way through the course. In particular, read carefully the note on How to Study Linear Algebra at the beginning of the Study Guide.  If you are purchasing your books through a different source, the Study Guide, though very useful, is optional.

There is some good supplementary material at the Companion Web Site for the course (http://www.laylinalgebra.com/).  In particular, there's a large collection review sheets and practice exams from the author.  (The practice exams may or may not be what our exams look like, but they certainly provide a good self-test on some of the material.)

You can also look at whatever material is available at MyMathLab: registration material should be included with the textbook.

• One goal in most upper level math courses is to develop clear writing and arguments, so the solution of each problem should be written up very clearly and legibly.  For the sake of the grader, be sure your writing is dark enough to be read easily.
• Solve problems first on scratchpaper; the use the scratchwork to write your hand-in solution.  The reader should never feel like s/he is reading your scratchwork.
• Write your solutions (calculations, proofs) as if the intended reader were an average student in the class.
• Check your mathematical style by reading aloud the words and symbols you wrote, exactly as written.  What you hear should be smooth-sounding English -- or else something is missing on paper!
• If necessary, rewrite the solution until you think it says what you want to say in a way that's clear and easy to read.