# MATH 204 - Fall 2018 Linear Algebra

Professor: Erika L.C. King
Email: eking@hws.edu
Office: Lansing 304
Phone: (315) 781-3355

Office Hours: M: 11:15am-12:15pm, W: 3:00-4:30pm, Th: 2:15-3:45pm, F: 3:00-4:00pm, and by appointment
Class Schedule: held MWF 1:55-2:50pm in Eaton 110
Course Syllabus

An online book for reviewing/learning about logic and proofs: Book of Proof by Richard Hammack
Proof Writing and Presentation Tips

### READING/EXAM WEEK: December 12 - December 18

BONUS WeBWorK due Tuesday, December 11 at 8:00pm:

• Practice material on Eigenvalues and Eigenvectors with the WeBWorK assignment here. This is good practice for the final exam. Be sure to read the directions and hints to help you understand what is being asked. Ask me if you have questions. This is due TUESDAY at 8:00pm!

• You should have a copy of the Final Exam Preparation sheet. If you have lost yours here is another copy.
• Reread Section 5.3 (pages 283-288). Do you feel confident with this material now?
• Complete the Practice Problem for Section 5.3 on page 288 of the text. This will not be collected, and you should check your answers on page 290.
• Complete these practice problems from Section 5.3 (pages 288-289): 3, 5, 11, 17, 21, 23, 25, 27 and 29. These will not be collected, but you should do ALL of these at least in your head if not on paper. In fact, you should do MORE odd problems if you are not confident after completing these! Note that AFTER you have solved these questions you can check your answers in the back of the textbook.

Review Session: Thursday, December 13th 10:30am-11:30am in Eaton 110. Bring questions!

Office Hours:

• Wednesday, December 12: 11:30am-1:30pm
• Friday, December 14: 1:30pm-3:30pm
• Monday, December 17: 11:00am-12:30pm
• By appointment

Final Exam: The final exam is on Monday, December 17th from 1:30PM until 4:30PM in Eaton 110 (our classroom).

HAVE A GREAT WINTER BREAK!!! KEEP IN TOUCH!!!

### WEEK 15: December 10 - December 14

There will be no quiz on the last day of class! :-)

Collected Homework (Due Monday, December 10 at 1:55pm):

• Note that these assignments are due right at the beginning of class! You must be on time and be ready to turn in your work - already stapled, etc. If you turn it in after 1:55 it is late and you will have to use your free late or lose points.
• Remember that although you may discuss this assignment with others, your write up should be your own. Do not share your write-up, look at other's write-ups, discuss word for word how something should be proved, etc. Be sure to note with whom you collaborate if you do.
• Complete the problems on this worksheet.
• This assignment is final (no additional questions were added on Friday)!

Homework for class Monday, December 10:

• Review your class notes from Friday's class and the cool proofs we did!
• Make sure you have completed this worksheet on the second half of Section 5.2 and Section 5.3. In particular, make sure you have worked through Section 5.3 Exercise 7 (question 7 on the handout). This will be a good warm-up for the one on your collected homework! Bring your work to class to discuss and present!
• Reread Section 5.2 (pages 276-281). Do you feel confident with this material now?
• Complete the Practice Problem for Section 5.2 on page 281 of the text. This will not be collected, and you should check your answers on page 283.
• Complete these practice problems from Section 5.2 (page 282): 9, 11, 13, 15, 17 and 21. These will not be collected, but you should do ALL of these at least in your head if not on paper. In fact, you should do MORE odd problems if you are not confident after completing these! Note that AFTER you have solved these questions you can check your answers in the back of the textbook.
• Reread Section 5.3 (pages 283-288) in your text. Keep track of what you understand and make of list of any questions you have.
• While rereading Section 5.3, make a note of Theorem 7 and try Exercise 19 on page 289, comparing it to Example 6. Doing this is essentially your reading-prep worksheet assignment for this class, but there are only two parts! Bring your work to class to discuss and present!
• Idea for reviewing for the final: Choose a partner. Each of you make up a practice exam using problems from the "Practice Problems" at the end of each section or odd numbered exercises in the text. Include 6-10 problems. Mix up the problems so that they don't necessarily appear in the same order as they are in the text. Exchange exams. Write up the solutions to each other's exams in a pseudo-test-taking atmosphere. Trade papers again and "grade" your partner's work! This might help you figure out which sections you need to focus on for studying!
• OPTIONAL (bonus!): Practice material on Eigenvalues and Eigenvectors with the WeBWorK assignment here. This is good practice for the final exam. Be sure to read the directions and hints to help you understand what is being asked. Ask me if you have questions. This is due TUESDAY at 8:00pm!

### WEEK 14: December 3 - December 7

Quiz 9 will take place on Monday at the beginning of class. It will cover Sections 4.4, 4.5 and 4.6. Be prepared to state definitions and theorems, give examples with explanations, and complete short exercises.

There will be time in class on Friday to complete course evaluations. If you have a laptop or other device on which it is easy to type, it would be useful to bring it on Friday for this purpose. I may also have a few devices.

Homework for class Monday, December 3:

• Review your class notes from Friday's class! Make a list of your questions, especially on Section 4.6. Come to office hours!
• Complete the Practice Problems for Section 4.5 on page 230 of the text. This will not be collected, and you should check your answers on page 232.
• Reread Section 4.6 (pages 232-238). Do you feel confident with this material now?
• Complete the Practice Problems for Section 4.6 on page 238 of the text. This will not be collected, and you should check your answers on page 240.
• Complete these practice problems from Section 4.6 (page 231): 3, 5, 7, 9, 11, 13, 15 and 17. These will not be collected, but you should do ALL of these at least in your head if not on paper. In fact, you should do MORE odd problems if you are not confident after completing these! Note that AFTER you have solved these questions you can check your answers in the back of the textbook.
• Read the motivation for Chapter 5 on pages 267-268 -- a real world owl application!
• Read what at least some of you have been waiting for!: Section 5.1 (pages 268-273) in your text. As you read, take notes, record questions and continue your list (or a set of flashcards!) of definitions, theorems and facts. You should also fill in the blanks for any skipped steps in the reading by working through calculations yourself!
• Complete this worksheet on Section 4.6 and 5.1. Bring your work to class to discuss and present!

Homework for class Wednesday, December 5:

• Review your class notes from Monday's class. Please let me know if you have any questions on the material we covered from Section 4.6.
• Reread Section 5.1 (pages 268-273) in your text. Keep track of what you understand and make of list of any questions you have.
• Make sure you have complete this worksheet on Section 4.6 and 5.1 that was due on Monday. We will start class with students being asked to put their solutions for questions 3 and 4 on the board.
• Read Section 5.2 (pages 276-281) in your text. As you read, take notes, record questions and continue your list (or a set of flashcards!) of definitions, theorems and facts. You should also fill in the blanks for any skipped steps in the reading by working through calculations yourself!
• Complete this worksheet on the second half of Section 5.1 and Section 5.2. Bring your work to class to discuss and present!

Homework for class Friday, December 7:

• Remember to bring, if possible, a laptop (or other device on which it is easy to type) to class on Friday to do course evaluations.
• Review your class notes from Wednesday's class. Great work on reading questions put on the board on Wednesday!
• Reread Section 5.1 (pages 268-273) in your text. Do you feel confident with this material now?
• Complete the Practice Problems for Section 5.1 on page 273 of the text. This will not be collected, and you should check your answers on pages 275-76.
• Complete these practice problems from Section 5.1 (page 273): 5, 9, 11, 13, 15, 19, 21 and 23. These will not be collected, but you should do ALL of these at least in your head if not on paper. In fact, you should do MORE odd problems if you are not confident after completing these! Note that AFTER you have solved these questions you can check your answers in the back of the textbook.
• Reread Section 5.2 (pages 276-281) in your text. Keep track of what you understand and make of list of any questions you have.
• Make sure you have completed this worksheet on the second half of Section 5.1 and Section 5.2. Bring your work to class to discuss and present! We talked about the outline of Theorem 5.2 on Wednesday, work on your outline before Friday's class.
• Read Section 5.3 (pages 283-288) in your text. As you read, take notes, record questions and continue your list (or a set of flashcards!) of definitions, theorems and facts. You should also fill in the blanks for any skipped steps in the reading by working through calculations yourself!
• Complete the first half of this worksheet on Sections 5.2 and 5.3. Bring your work to class to discuss and present!

Our last collected homework assignment will be due on MONDAY!

### WEEK 13: November 26 - November 30

Have a great Thanksgiving Break!!!

Since we had an exam in our last class, there will be NO quiz this week!

Due to needing to visit another professor's class, I must cancel my Monday office hours on November 26th. If you would like to meet with me before my Wednesday office hours, please email me and we will find another time to meet!

Homework for class Monday, November 26:

• Review your class notes from Wednesday the 14th's class on the proof of Theorem 4.7.
• Read all of Section 4.4 in your text (pages 218-224). As you read, take notes, record questions and continue your list (or a set of flashcards!) of definitions. You should fill in the blanks for any skipped steps in the reading by working through calculations yourself!
• If you haven't finished the reading prep sheet that was assigned for Wednesday the 14th, do it now! Bring your work to class to discuss and present!
• Complete this worksheet to cover the last few pages of Section 4.4. Bring your work to class to discuss and present!
• Complete the Practice Problems for Section 4.4 on page 224 of the text. This will not be collected, and you should check your answers on pages 226-227.

Homework for class Wednesday, November 28:

• Review your class notes from Monday's class. Write down any questions you have about the material from Section 4.4 so that you can ask them in office hours or class.
• Read Section 4.5 (pages 227-230) in your text (this is really just two pages!). The ideas of ${\mathbb R}^n$ as a vector space give us some intuition into this idea of dimension! As you read, take notes, record questions and continue your list (or a set of flashcards!) of definitions, theorems and facts. You should also fill in the blanks for any skipped steps in the reading by working through calculations yourself!
• Complete this worksheet on Section 4.5. Bring your work to class to discuss and present!
• Complete these practice problems from Section 4.4 (pages 224-225): 3, 7, 9, 13, 15, 19, 21, 23, 27 and 29. These will not be collected, but you should do ALL of these at least in your head if not on paper. In fact, you should do MORE odd problems if you are not confident after completing these! Note that AFTER you have solved these questions you can check your answers in the back of the textbook.
• Review Exam 3, reworking any problems on which you missed points. Make sure you feel comfortable with these questions and come to office hours with questions if you do not feel confident with any of the material.

Collected Homework (Due Friday, November 30 at 1:55pm):

• Note that these assignments are due right at the beginning of class! You must be on time and be ready to turn in your work - already stapled, etc. If you turn it in after 1:55 it is late and you will have to use your free late or lose points.
• Remember that although you may discuss this assignment with others, your write up should be your own. Do not share your write-up, look at other's write-ups, discuss word for word how something should be proved, etc. Be sure to note with whom you collaborate if you do.
• Complete the problems on this worksheet.
• This was finalized on Wednesday of Week 13 with one additional problem!

Homework for class Friday, November 30:

• Review your class notes from Wednesday's class. Gather any questions you have about Section 4.5, and bring them to office hours or class!
• Complete these practice problems from Section 4.5 (page 231): 5, 9, 11, 15, 19, 21, 23 and 25. These will not be collected, but you should do ALL of these at least in your head if not on paper. In fact, you should do MORE odd problems if you are not confident after completing these! Note that AFTER you have solved these questions you can check your answers in the back of the textbook.
• Read Section 4.6 (pages 232-238) in your text. As you read, take notes, record questions and continue your list (or a set of flashcards!) of definitions, theorems and facts. You should also fill in the blanks for any skipped steps in the reading by working through calculations yourself!
• Complete this worksheet on Section 4.6. Bring your work to class to discuss and present!

### WEEK 12: November 12 - November 16

Quiz 8 will take place on Monday at the beginning of class. It will cover Sections 4.2 and 4.3. Be prepared to state definitions and theorems, give examples with explanations, and complete short exercises.

Homework for class Monday, November 12:

• Review your class notes from Friday's class. Please let me know if you have any questions on the material we covered from Section 4.3.
• Work through the group worksheet from Friday. Be ready to put your results on the board as soon as the quiz is over.
• Complete these practice problems from Section 4.2 (page 209): 31, 32 and 35. These will not be collected, but you should do ALL of these at least in your head if not on paper. In fact, you should do MORE odd problems if you are not confident after completing these! Note that AFTER you have solved these questions you can check your answers in the back of the textbook.
• Complete this worksheet. Bring your work to class to discuss and present! Note that this is a SHORT worksheet, so you should have time to work on the group worksheet and have lots of details to share!!! (It is ok if those details are questions as well as answers, but you should spend significant time on the group worksheet!)
• Complete the Practice Problems for Section 4.3 on page 215 of the text. This will not be collected, and you should check your answers on pages 209-210.

Homework for class Wednesday, November 14:

• Review your class notes from Monday's class, and make sure you have finished working through the group worksheet from Friday/Monday.
• Practice material on Bases, Null Spaces and Column Spaces with the WeBWorK assignment here. Be VERY careful! The first two only allow TWO submissions! Be sure to read the directions and hints to help you understand what is being asked. Ask me if you have questions. This is due Wednesday at 1:00pm.
• Each group wrote a problem from the group worksheet on the board on Monday. If your group wrote up parts (c), (e), (f) or (g), be sure to connect with your group and put your solution up on the board as soon as you arrive in class on Wednesday.
• Read pages 218-221 of Section 4.4 in your text. As you read, take notes, record questions and continue a list (or a set of flashcards!) of definitions. You should also fill in the blanks for any skipped steps in the reading by working through calculations yourself!
• Complete this worksheet. Bring your work to class to discuss and present!
• Complete these practice problems from Section 4.3 (pages 215-217): 5, 7, 9, 11, 15, 19, 21, 23 and 29. These will not be collected, but you should do ALL of these at least in your head if not on paper. In fact, you should do MORE odd problems if you are not confident after completing these! Note that AFTER you have solved these questions you can check your answers in the back of the textbook.
• Email me any questions you have on any of the material in Sections 3.2 and 4.1-4.3 by noon on Wednesday! This includes any questions you have on past due WeBWorKs. (I am happy to address questions on the WeBWorK due Thursday individually.) Even if you don't have time to email me, bring the questions to class. We will be able to address more questions if I know what they are ahead of time. You are also highly encouraged to ask questions in office hours!!!
• This is listed below as well since it is not actually due on Wednesday: ALSO practice material on Bases, Null Spaces and Column Spaces with the WeBWorK assignment here. This is good practice for the exam on Friday! Be sure to read the directions and hints to help you understand what is being asked. Ask me if you have questions. This is due THURSDAY at 1:00pm, but I highly recommend that you complete it sooner!

WeBWorK due Thursday, November 15 at 1:00pm:

• I think this is a good check as you study for your exam, but instead of making it due Wednesday, I extended it to Thursday so that you can choose when you want to focus on this material.
• Practice material on Bases, Null Spaces and Column Spaces with the WeBWorK assignment here. This is good practice for the exam on Friday! Be sure to read the directions and hints to help you understand what is being asked. Ask me if you have questions. This is due THURSDAY at 1:00pm!

Since we have an exam on Friday, there will be NO collected homework due on Friday!!!

Homework for class Friday, November 16:

• Finish preparing for Exam 3!
• You should have a copy of the Exam 3 Preparation sheet. If you have lost yours here is another copy.
• Be sure to do extra practice problems with any material for which you feel less comfortable. Make sure you are confident when you come to class on Monday!
• REMEMBER TO BE AT THE EXAM IN EATON 110 AT 1:25!!! Also, as it says on the syllabus, seats will be randomized for the exam. So don't get too settled before the names are set out.

### WEEK 11: November 5 - November 9

Quiz 7 will take place on Monday at the beginning of class. It will cover Sections 4.1 and 4.2. Be prepared to state definitions and theorems, give examples with explanations, and complete short exercises.

Homework for class Monday, November 5:

• Practice material on Subspaces with the WeBWorK assignment here. Be VERY careful! The first three only allow ONE submission! Be sure to read the directions and hints to help you understand what is being asked. Ask me if you have questions. This is due Monday at 1:00pm.
• Review your class notes from Friday's class. Please let me know if you have any questions on the material we covered from Sections 4.1 and 4.2.
• In class we proved two parts of Theorem 4.2. Finish proving the other two parts (closure under vector addition and scalar multiplication)! Be ready to share your results and write them on the board!
• If you haven't worked through problems 2-4 on the group worksheet handed out on Wednesday, do so now. These are great examples for understanding subspaces and preparing for future exams.
• Read/reread Section 4.2 in your text (pages 200-207). As you read, take notes, record questions and work on your list (or a set of flashcards!) of definitions. For example, you should know the definitions of null space and column space. You should also feel free to fill in the blanks for any skipped steps in the reading by working through calculations yourself!
• Complete the Practice Problems for Section 4.2 on page 207 of the text. This will not be collected, and you should check your answers on pages 209-210.
• Complete this worksheet. Bring your work to class to discuss and present!

Homework for class Wednesday, November 7:

• Make sure you completed this worksheet that was due on Monday; you need these details in your mind. Really write them down!!!
• Finish working through the group worksheet we were doing at the end of class. Go directly to your groups when you get to class and be ready to share your solutions on the board. Note that there is no reading prep worksheet (although you SHOULD start reading Section 4.3 as assigned below!) due Wednesday so it is expected that you DO spend significant time on this group worksheet!
• Reread Section 4.2 in your text (pages 200-207). Where do you still have questions and where have questions been cleared up for you?
• Complete these practice problems from Section 4.2 (pages 208-209): 3, 5, 9, 11, 15, 17, 21, 23 and 25. These will not be collected, but you should do ALL of these at least in your head if not on paper. In fact, you should do MORE odd problems if you are not confident after completing these! Note that AFTER you have solved these questions you can check your answers in the back of the textbook.
• Read pages 210-212 of Section 4.3 in your text. As you read, take notes, record questions and start a list (or a set of flashcards!) of definitions. For example, you should know the definitions of basis and standard basis. You should also feel free to fill in the blanks for any skipped steps in the reading by working through calculations yourself!

BONUS ASSIGNMENT due Thursday, November 8 by 3:30pm:

You may earn up to 5 points back on your second exam. Please read this in detail if you wish to earn points! Here are the rules:
• No collaboration allowed. You may not discuss these bonus submissions with anyone but Professor King. You are highly encouraged to discuss them with Professor King!
• No outside resources allowed. You may only use your notes and the textbook.
• After your solution, write "I did not collaborate or use outside resources on this bonus assignment." and then sign it.
• If you lost five or more points on question 9 or question 10, write a new solution to that problem. If you missed five or more points on both questions, you may choose which to submit for the bonus assignment. If you missed less than five points on both questions 9 and 10, then submit a solution to one of the exam bonus problems for which you received no points on the exam.
• You must staple your resubmission to your original exam before turning it in.
• Since this is for bonus points, I will be looking for much more detail than I did on the exam where you had little time for reflection.

Collected Homework (Due Friday, November 9 at 1:55pm):

• Note that these assignments are due right at the beginning of class! You must be on time and be ready to turn in your work - already stapled, etc. If you turn it in after 1:55 it is late and you will have to use your free late or lose points.
• Remember that although you may discuss this assignment with others, your write up should be your own. Do not share your write-up, look at other's write-ups, discuss word for word how something should be proved, etc. Be sure to note with whom you collaborate if you do.
• Complete the problems on this worksheet.

Homework for class Friday, November 9:

• Review your class notes from Wednesday's class. Make sure you have all the details on your group worksheet. Please let me know if you have any questions on the material we covered from Section 4.2.
• Read Section 4.3 in your text (pages 210-215). As you read, take notes, record questions and continue your list (or a set of flashcards!) of definitions and theorems. For example, you should know the definitions of basis and standard basis, and the statements of Theorems 4.4-4.6. You should also fill in the blanks for any skipped steps in the reading by working through calculations yourself!
• Complete this worksheet. Bring your work to class to discuss and present!
• Complete these practice problems from Section 4.2 (page 209): 31, 32 and 35. These will not be collected, but you should do ALL of these at least in your head if not on paper. In fact, you should do MORE odd problems if you are not confident after completing these! Note that AFTER you have solved these questions you can check your answers in the back of the textbook.

### WEEK 10: October 29 - November 2

Quiz 6 will take place on Monday at the beginning of class. It will cover Section 3.2 and the beginning of 4.1. Be prepared to state definitions and theorems, give examples with explanations, and complete short exercises.

Homework for class Monday, October 29:

• Review your class notes and group work solutions from Friday's class. Make sure you understand the proof by induction. Isn't it neat how it all fits together! Also complete any parts of the group worksheet that you did not complete in class.
• Practice material on Determinants with the WeBWorK assignment here. Most of these should be a quick! Be sure to read the directions and hints to help you understand what is being asked. This is due Monday at 1:00pm.
• Complete this worksheet. Bring your work to class to discuss and present! Note there is a place on the worksheet to write down your questions!
• Complete the Practice Problems for Section 4.1 on page 197 of the text. This will not be collected, and you should check your answers on page 200.

Homework for class Wednesday, October 31: Happy Halloween!!!:

• There was a question about number nine on the WeBWorK problem set due Monday. Look back at this question and justify your answers for each statement. Be ready to discuss this in class!
• Review your notes from Monday's class. Be sure to work through the proofs of the other six axioms for the polynomial example!
• Finish the group worksheet from Monday's class. Be ready to discuss each question carefully.
• Reread Section 4.1 in your text (pages 192-197). Where do you still have questions and where have questions been cleared up for you?
• Complete these practice problems from Section 4.1 (pages 198-199): 3, 5, 7, 9, 11 and 27. These will not be collected, but you should do ALL of these at least in your head if not on paper. In fact, you should do MORE odd problems if you are not confident after completing these! Note that AFTER you have solved these questions you can check your answers in the back of the textbook.
• Read pages 200-203 of Section 4.2 in your text. As you read, take notes, record questions and start a list (or a set of flashcards!) of definitions. For example, you should know the definitions of null space and column space. You should also fill in the blanks for any skipped steps in the reading by working through calculations yourself!
• Complete this worksheet. Bring your work to class to discuss and present!

Collected Homework (Due Friday, November 2 at 1:55pm):

• Note that these assignments are due right at the beginning of class! You must be on time and be ready to turn in your work - already stapled, etc. If you turn it in after 1:55 it is late and you will have to use your free late or lose points.
• Remember that although you may discuss this assignment with others, your write up should be your own. Do not share your write-up, look at other's write-ups, discuss word for word how something should be proved, etc. Be sure to note with whom you collaborate if you do.
• Complete the problems on this worksheet.

Homework for class Friday, November 2:

• Review your notes from Wednesday's class. Please let me know if you have any questions on the material we covered from Section 4.1. Be sure to finish proving Theorem 4.1; you need the proof that the span is closed under scalar multiplication.
• Make sure you completed this worksheet that was due on Wednesday; we only discussed questions 1 and 2, so be ready with the rest! Be ready to be called upon to share your work!
• Work on detailed proofs of the axioms in Problem 1 of the group worksheet I handed out at the end of class. Be ready to put these on the board!
• Problems 2-5 on the group worksheet are about subspaces. Outline solutions for these exercises.

### WEEK 9: October 22 - October 26

Homework for class Monday, October 22:

• Finish preparing for Exam 2!
• You should have a copy of the Exam 2 Preparation sheet. Here is another copy. Note that you can find the full statements of all the Theorems and Facts in boxes in your text. Note that these are all things you should know and you should use. They will not be given to you with the exam.
• Feel free to email me with questions any time over the weekend!!! Remember that I also have office hours on Monday morning.
• REMEMBER TO BE AT THE EXAM IN EATON 110 AT 1:25!!! Also, as it says on the syllabus, seats will be randomized for the exam. So don't get too settled before the names are set out.

Homework for class Wednesday, October 24:

• The text gives a very brief summary of induction in the paragraph before Theorem 3.5 on page 174. This is insufficient for understanding the technique. If you are new to induction or it is just feeling a bit rusty, check out the first three pages of this chapter of Richard Hammack's book, Book of Proof. We will be using induction to prove Theorem 3.2 on page 169.
• Complete these practice problems from Section 3.1 (pages 170-171): 11, 17, 25, 27, 29, 37, 39 and 40. These will not be collected, but you should do ALL of these at least in your head if not on paper. In fact, you should do MORE odd problems if you are not confident after completing these! Note that AFTER you have solved these questions you can check your answers in the back of the textbook.
• Complete the Practice Problems for Section 3.2 on pages 176-177 of the text. This will not be collected, and you should check your answers on page 179.
• If you did not finish the reading worksheet that was due on Friday, do it now! Be ready to discuss this and put solutions on the board!
• Complete this shorter reading worksheet on Section 3.2. Bring your work to class to discuss and present! Note there is a place on the worksheet to write down your questions! You will need your reading worksheets completed in order to do the group work!

Collected Homework (Due Friday, October 26 at 1:55pm):

• Note that these assignments are due right at the beginning of class! You must be on time and be ready to turn in your work - already stapled, etc. If you turn it in after 1:55 it is late and you will have to use your free late or lose points.
• Remember that although you may discuss this assignment with others, your write up should be your own. Do not share your write-up, look at other's write-ups, discuss word for word how something should be proved, etc. Be sure to note with whom you collaborate if you do.
• Complete the problems on this worksheet.

Homework for class Friday, October 26:

• Review your notes from Wednesday's class. Make an outline of the proof by induction for Theorem 3.2 that we started. Review the group work that we did in class and let me know if you have any questions.
• Reread Section 3.2 (pages 171-176). Note especially the process in example 2 for finding a determinant using scaling. This will help you for your homework due on Friday.
• Complete these practice problems from Section 3.2 (pages 177-178): 21, 25, 27, 28, 35 and 39. These will not be collected, but you should do ALL of these at least in your head if not on paper. In fact, you should do MORE odd problems if you are not confident after completing these! Note that AFTER you have solved these questions you can check your answers in the back of the textbook.
• Read the motivation for Chapter 4 on pages 191-192.
• Read pages 192-193 of Section 4.1 in your text (JUST TWO PAGES!). As you read, take notes, record questions and start a list (or a set of flashcards!) of definitions. For example, you should know the definition of vector space. You should also fill in the blanks for any skipped steps in the reading by working through calculations yourself!
• Complete this worksheet on Section 4.1. Bring your work to class to discuss and present! Note there is a place on the worksheet to write down your questions!

### WEEK 8: October 15 - October 19

Quiz 5 will take place on Monday at the beginning of class. It will cover Sections 2.1 and 2.2. Be prepared to state definitions and theorems, give examples with explanations, and complete short exercises.

Homework for class Monday, October 15:

• Review your class notes from Friday's class.
• Complete these practice problems from Section 2.2 (pages 111-113): 9, 11 ($X$ is a matrix. This is good practice in proving uniqueness: first prove that it is a solution and then assume two solutions exist and show they must be the same. See our work in class or the proof of Theorem 5 in the text for examples.), 13, 15 (this is generalizing the Shoes and Socks Theorem!), 17 and 21. These will not be collected, but you should do ALL of these at least in your head if not on paper. In fact, you should do MORE odd problems if you are not confident after completing these! Note that AFTER you have solved these questions you can check your answers in the back of the textbook.
• If you did not finish the reading worksheet that was due on Friday, do it now! Be ready to discuss this and put solutions on the board!
• Complete this worksheet. Bring your work to class to discuss and present! Note there is a place on the worksheet to write down your questions!

BONUS ASSIGNMENT due Wednesday, October 17 at 1:55pm:

You may rewrite the proof of the second problem from the homework for Week 5 to win points toward your homework score. This is a chance to practice proof writing. Here are the rules:
• No collaboration allowed. You may not discuss these rewrites with anyone but Professor King. You are highly encouraged to discuss them with Professor King!
• No outside resources allowed. You may only use your notes and the textbook.
• If you earned full credit on this problem, you must talk to me about redoing a different problem!
• Since this is for bonus points, I will be looking for even more detail and precision than on a regular assignment, but it should be concise.
• You can earn up to four points no matter how many you lost on your original submission (and even if you did not turn in the assignment originally!). Be sure to read my comments on your graded work!
• No bonus assignments will be accepted after 1:55. No exceptions!

Homework for class Wednesday, October 17:

• Review your notes from Monday's class. In particular, review the group work problems and make sure they all make sense.
• Practice material on Elementary Matrices with the WeBWorK assignment here. Many of these should be a quick check of your understanding. Be sure to read the directions and hints to help you understand what is being asked. This is due Wednesday at 1:00pm.
• If you did not finish the reading worksheet that was due on Monday, do it now! Be ready to discuss this and put solutions on the board!
• Reread Section 2.3 in your text (pages 113-116). Particularly work through the details of the proof of Theorem 2.9 using the text as a guide, but making sure to fill in details the text left out. Do you have any questions?
• Complete the Practice Problems for Section 2.3 on page 116 of the text. This will not be collected, and you should check your answers on pages 118-119.
• We know how to find the determinate of a $2\times 2$ matrix. Now we will learn how to find determinants of larger matrices. Read pages 166-167 of Section 3.1 in your text. Yes, we are skipping ahead! This is technical so I am only asking you to read the first two pages so that you can work on understanding the notation.
• Complete this short(!) worksheet. Bring your work to class to discuss and present! Note there is a place on the worksheet to write down your questions!

Collected Homework (Due Friday, October 19 at 1:55pm):

• Note that these assignments are due right at the beginning of class! You must be on time and be ready to turn in your work - already stapled, etc. If you turn it in after 1:55 it is late and you will have to use your free late or lose points.
• Remember that although you may discuss this assignment with others, your write up should be your own. Do not share your write-up, look at other's write-ups, discuss word for word how something should be proved, etc. Be sure to note with whom you collaborate if you do.
• Complete the problems on this worksheet.
• The above assignment was originally posted on Monday afternoon. It was finalized on Tuesday afternoon!

Homework for class Friday, October 19:

• Review your notes from Wednesday's class. We worked through the one part of the proof of Theorem 2.9; now make sure the rest of the proof makes sense too. Write down any questions you still have and ask them either in class or in office hours or through email! Do not let any question, no matter how small, go unanswered!
• Make sure you have worked through the worksheet that was due on Wednesday.
• Look back at the proof of Theorem 7 on page 109. Carefully study how Theorem 6 was vital to the result.
• Complete the ONE Practice Problem for Section 3.1 on page 169 of the text. This will not be collected, and you should check your answers on page 171.
• Complete these practice problems from Section 2.3 (pages 117-118): 11, 15, 17, 21, 27 and 31. These will not be collected, but you should do ALL of these at least in your head if not on paper. In fact, you should do MORE odd problems (or even - these are GREAT QUESTIONS!!!) if you are not confident after completing these! Note that AFTER you have solved these questions you can check your answers in the back of the textbook.
• Complete this worksheet on Section 3.1 and 3.2. Bring your work to class to discuss and present! Note there is a place on the worksheet to write down your questions!

### WEEK 7: October 10 - October 12

Have a Great Fall Break!!!

Since we have fall break this week, we will NOT have a quiz this week!

Homework for class Wednesday, October 11:

• Review your notes from class. In particular, review the group work problems and make sure they all make sense.
• Write up a short proof for 2(g) from the group work. (This is proving Theorem 3(d)!) Try looking at the $(i,j)$-entry of each matrix. Use your notation! Be ready to put your proof on the board!
• Complete these practice problems from Section 2.1 (pages 102-103): 5, 7, 8, 9, 10, 23 and 25 (this is a great problem!). These will not be collected, but you should do ALL of these at least in your head if not on paper. In fact, you should do MORE odd problems if you are not confident after completing these! Note that AFTER you have solved these questions you can check your answers in the back of the textbook.
• If you did not finish the reading worksheet that was due on Friday, do it now! Be ready to discuss this and put solutions on the board!
• Read Section 2.2 in your text (pages 104-111). As you read, take notes, record questions and work on your list (or a set of flashcards!) of definitions. You should also fill in the blanks for any skipped steps in the reading by working through calculations yourself!
• Complete this worksheet. Bring your work to class to discuss and present! Note there is a place on the worksheet to write down your questions!

Collected Homework (Due Friday, October 12 at 1:55pm):

• Note that these assignments are due right at the beginning of class! You must be on time and be ready to turn in your work - already stapled, etc. If you turn it in after 1:55 it is late and you will have to use your free late or lose points.
• Remember that although you may discuss this assignment with others, your write up should be your own. Do not share your write-up, look at other's write-ups, discuss word for word how something should be proved, etc. Be sure to note with whom you collaborate if you do.
• Complete the problems on this worksheet.
• The above assignment was originally posted on Friday afternoon. It was finalized on Wednesday afternoon!

Homework for class Friday, October 12:

• Carefully read through your Exam 1 and rework any questions on which you lost points. Come to office hours to go over any questions you have. Everyone should do this no matter how few points you missed! We will start class on Friday by going over a few of the questions. As I said in class, I would like the following people to put their solutions for the corresponding questions on the board as soon as you arrive in class: Edgar (2c), Andy (4), Alex (6a), Lindsey (6b), Anna (6c) and Hamdan (6d). Note that I have asked you to rework question 5 for your collected homework due on Friday.
• Review your notes from class. Write down any questions you still have and ask them either in class or in office hours or through email! Do not let any question, no matter how small, go unanswered!
• If you did not finish the last two pages of the reading worksheet that was due on Monday, do it now! Be ready to discuss this and put solutions on the board!
• Complete the Practice Problems for Section 2.2 on page 111 of the text. This will not be collected, and you should check your answers on page 113.
• Complete this worksheet. Bring your work to class to discuss and present! Note there is a place on the worksheet to write down your questions!
• Read Section 2.3 in your text (pages 113-116). This is really only three pages!

### WEEK 6: October 1 - October 5

Quiz 4 will take place on Monday at the beginning of class. It will cover Sections 1.8 and the beginning of 1.9. Be prepared to state definitions and theorems, give examples with explanations, and complete short exercises.

Homework for class Monday, October 1:

• Reread Section 1.8 in your text (pages 63-69), and review your class notes from Friday's class. Do you have any questions?
• Reread Section 1.9 in your text (pages 71-78). If you did not complete the worksheet that was due on Friday, do it now.
• Review Theorem 10 and work through the proof of existence. Follow the text and fill in any missing parts.
• Complete this worksheet on the end of Section 1.9 and bring your work to class to discuss and present!
• Read the motivation for Chapter 2 on pages 93-94. Aircraft Design!!!
• Read pages 94-98 of Section 2.1. Take notes and write down any questions you have. This section is about Matrix Operations. Now we will look at operations with not only a matrix and a vector, but with two matrices (where the second is more than just an $n \times 1$ matrix)! See how these operations work similarly to real numbers, and how they are different.

Homework due Wednesday, October 3:

• Review your notes from class on Monday and the worksheets we discussed. Review the three standard matrices we discussed at the end of class, and make sure you see how we were able to determine whether or not they correlated to one-to-one or onto linear transformations. Can you come up with a specific example that shows why $A_1$ correlates to a linear transformation that is not one-to-one? Be ready to share your example with the class.
• See if you can come up with a standard matrix that correlates to a linear transformation that is one-to-one but not onto. Justify that your example works or show that none can be found. Be ready to share your example with the class.
• Practice material on Linear Transformations with the WeBWorK assignment here. Many of these should be a quick check of your understanding. This is due Wednesday at 1:00pm.
• Complete the Practice Problems for Section 1.9 on page 78 of the text. This will not be collected, and you should check your answers on pages 80-81.
• Complete these practice problems from Section 1.9 (pages 69-70): 3, 9, 17, 19, 21, 23, 25, 27, 29, 31 and 35. These will not be collected, but you should do ALL of these at least in your head if not on paper. In fact, you should do MORE odd problems if you are not confident after completing these! Note that AFTER you have solved these questions you can check your answers in the back of the textbook.
• Reread/read Section 2.1 in your text (pages 94-102). As you read, take notes, record questions and start a list (or a set of flashcards!) of definitions. You should also fill in the blanks for any skipped steps in the reading by working through calculations yourself!
• Complete this worksheet on Section 2.1 and bring your work to class to discuss and present! This is meant to help to guide and direct you through the reading and beginning to comprehend the new material. Note questions you have as you are working through these!

Collected Homework (Due Friday, October 5 at 1:55pm):

• Note that these assignments are due right at the beginning of class! You must be on time and be ready to turn in your work - already stapled, etc. If you turn it in after 1:55 it is late and you will have to use your free late or lose points.
• Remember that although you may discuss this assignment with others, your write up should be your own. Do not share your write-up, look at other's write-ups, discuss word for word how something should be proved, etc. Be sure to note with whom you collaborate if you do.
• Complete the problems on this worksheet.
• The above assignment was originally posted on Friday afternoon. It was updated on Tuesday afternoon at 3:50, and finalized on Wednesday!

Homework for class Friday, October 5:

• Review your notes from class particularly the proof of Theorem 11. Write down any questions that you have.
• Read the proof of Theorem 12 on page 78 in your text. Fill in any blanks and make sure it makes sense to you. Notice how this proof uses theorems and facts!
• Complete the Practice Problems for Section 2.1 on page 102 of the text. This will not be collected, and you should check your answers on page 104.
• If you did not finish the reading worksheet that was due on Wednesday, do it now! Be ready to put your solutions on the board when you arrive in class on Friday!
• Complete this worksheet. As with the worksheet that was due on Wednesday, bring your work to class to discuss and present!

### WEEK 5: September 24 - September 28

Homework for class Monday, September 24:

• Finish preparing for Exam 1!
• You should have a copy of the Exam 1 Preparation sheet. Here is another copy. Also, here is the Chapter 1 Theorems and Facts sheet. Note that you can find the full statements of all the Theorems and Facts in boxes in your text except for Facts 2 a and b. Those we have used multiple times, but they are not explicitly stated in the text. I included them so that you could use them without having to justify them. Note that these are all things you should know and you should use. They will not be given to you with the exam.
• Feel free to email me with questions any time over the weekend!!! Remember that I also have office hours on Monday morning.
• REMEMBER TO BE AT THE EXAM IN EATON 110 AT 1:25!!! Also, as it says on the syllabus, seats will be randomized for the exam. So don't get too settled before the names are set out.

Homework for class Wednesday, September 26:

• Read Section 1.8 in your text (pages 63-69). As you read, take notes, record questions and start a list (or a set of flashcards!) of definitions.
• Complete the Practice Problems on page 69 of the text. This will not be collected, and you should check your answers on page 71.
• Complete this worksheet on Section 1.8 and bring your work to class to discuss and present! Do the best you can with each part. Some parts of the reading assignment will be easier to complete than others. You should at least have all the definitions and attempt the other questions.

Collected Homework (Due Friday, September 28 at 1:55pm):

• Note that these assignments are due right at the beginning of class! You must be on time and be ready to turn in your work - already stapled, etc. If you turn it in after 1:55 it is late and you will have to use your free late or lose points.
• Remember that although you may discuss this assignment with others, your write up should be your own. Do not share your write-up, look at other's write-ups, discuss word for word how something should be proved, etc. Be sure to note with whom you collaborate if you do.
• Complete the problems on this worksheet.
• Note that some of these problems will be clearer after our class on Wednesday!
• FREE LATE! I will allow you to turn these in up to 1:00pm on Sunday. This is a free free late! You may want to finish the third question after our class on Friday. Note, I will NOT accept homework at the end of class. That is, you should not be working on it during class. You should either submit it by 1:55pm on Friday, or bring it to my office after you have completed it later that day or Saturday or Sunday by 1pm.

Homework for class Friday, September 28:

• Review your notes from class and the worksheets we discussed. Make sure you have worked through the last two problems on the reading worksheet that was due on Wednesday. We did half of question 7 and discussed approaches to solving question 8. See if you can solve question 8 in two ways!
• Complete these practice problems from Section 1.8 (pages 69-70): 1, 5, 9, 15, 17, 21 and 31. These will not be collected, but you should do ALL of these at least in your head if not on paper. In fact, you should do MORE odd problems if you are not confident after completing these! Note that AFTER you have solved these questions you can check your answers in the back of the textbook.
• Read Section 1.9 in your text (pages 71-78). As you read, take notes, record questions and expand your list (or a set of flashcards!) of definitions. For example, you should know the definitions of the standard matrix of a transformation, one-to-one, onto, etc. You should also feel free to fill in the blanks for any skipped steps in the reading by working through calculations yourself!
• Complete this worksheet on Section 1.9 and bring your work to class to discuss and present!

### WEEK 4: September 17 - September 21

Quiz 3 will take place on Monday at the beginning of class. It will cover Sections 1.4 and 1.5. Be prepared to state definitions and theorems, give examples with explanations, and complete short exercises.

Homework for class Monday, September 17:

• If you are still having questions about row reduction, check out this video!
• Review your notes from Friday's class (including the proof of Theorem 4) and the worksheet we discussed. Bring your questions to office hours and class. Do you have any questions about the form or the logic of our proof?
• Complete these practice problems from Section 1.5 (pages 48-49): 17, 19, 31, 33 and 23.
• Read Section 1.7 in your text (pages 56-61). As you read, take notes, record questions and start a list (or a set of flashcards!) of definitions. You should also feel free to fill in the blanks for any skipped steps in the reading by working through calculations yourself!
• Complete this worksheet on Section 1.7 and bring your work to class to discuss.

Homework for class Wednesday, September 19:

• Review the problems we worked on in class on Monday as well as the material (especially Theorem 6!) we discussed from Section 1.5.
• Reread Section 1.7 in your text (pages 56-61). Review your flashcards and other notes! Write down questions to bring to class. If you have not finished the worksheet that was due for Monday, make sure you finish it now.
• Complete the Practice Problems for Section 1.7 on page 61 of the text. This will not be collected, and you should check your answers on page 63.
• Complete this worksheet on Section 1.7 and bring your work to class to discuss.

Collected Homework (Due Friday, September 21 at 1:55pm):

• Note that these assignments are due right at the beginning of class! You must be on time and be ready to turn in your work - already stapled, etc. If you turn it in after 1:55 it is late and you will have to use your free late or lose points.
• Remember that although you may discuss this assignment with others, your write up should be your own. Do not share your write-up, look at other's write-ups, discuss word for word how something should be proved, etc. Be sure to note with whom you collaborate if you do.
• Complete the problems on this worksheet.
• The above worksheet has been finalized! The first two problems were posted Monday and the rest was posted on Tuesday.

Homework for class Friday, September 21:

• Remember to come to office hours with any questions you have! Review your class notes from our discussions and problem sets. Make a list of specific questions that you can ask in office hours. You can also ask some questions in class as well, but you should not save all of your questions for class as others may have some as well. The exam on Monday will cover Sections 1.1-1.5 and 1.7. I will provide a review sheet with a list of Theorems and Facts you should know on Friday.
• Practice material in Section 1.7 with the WeBWorK assignment here. The theorems from Section 1.7 will be very helpful here!!! In order to not have too much due on Friday, this is due Saturday at 6:00pm. These questions are a good review for the exam!
• Reread Section 1.7 in your text (pages 56-61). Review your flashcards and other notes! If you have not finished the worksheets that were due Monday and Wednesday, make sure you finish them now.
• Be sure you complete the practice problems we started in class on Wednesday from Section 1.7 (page 62): 11, 15, 17, 19, 21, 23, 27 and 31. Also try exercises 33 and 35. These will not be collected, but you should do ALL of these at least in your head if not on paper. In fact, you should do MORE odd problems if you are not confident after completing these! Note that AFTER you have solved these questions you can check your answers in the back of the textbook.

### WEEK 3: September 10 - September 14

Quiz 2 will take place on Monday at the beginning of class. It will cover Sections 1.2 and 1.3. Be prepared to state definitions and theorems, give examples with explanations, and complete short exercises.

Due to needing to visit another professor's class, I must cancel my Monday office hours. If you would like to meet with me before my Wednesday office hours, please email me and we will find another time to meet!

Homework for class Monday, September 10:

• Practice material in Sections 1.3 and 1.4 with the WeBWorK assignment here. It isn't as long as it looks! But be very careful about how many attempts you have for each question!!! This is due Monday at 1:00pm.
• Review your notes from class and the worksheet we discussed. Bring your questions to office hours and class.
• Reread Section 1.4 in your text (pages 35-40). Write down questions to bring to class.
• Complete the second side of the group work sheet we were working on in class on Friday. This is on Theorem 4 and matrix equations. Bring your work to class to share and discuss.
• Complete the Practice Problems on page 40 of the text. This will not be collected, and you should check your answers on pages 42-43.
• If you didn't complete the Section 1.3 practice problems assigned for Friday, do them now. Then try these practice problems from Section 1.3 (pages 32-33): 23 and 24. Be sure you can explain why the statements are true or false.

Homework for class Wednesday, September 12:

• We are going to back track a bit to make sure we all feel comfortable with this material. Reread Section 1.4 in your text (pages 35-40). Write down questions to bring to class.
• Complete this worksheet on Section 1.4 and bring your work to class to discuss. Some of these things we already discussed in class, but here is a chance to review it.
• Complete these practice problems from Section 1.4 (pages 40-42): 1, 5, 7, 9, 11, 13, 15, 17, 21, 23 and 25. These will not be collected, but you should do ALL of these at least in your head if not on paper. In fact, you should do MORE odd problems if you are not confident after completing these! Note that AFTER you have solved these questions you can check your answers in the back of the textbook.
• Start reading Section 1.5 in your text (pages 43-47). There will be a reading worksheet for this section due on Friday.

Collected Homework (Due Friday, September 14 at 1:55pm):

• Remember that although you may discuss this assignment with others, your write up should be your own. Do not share your write-up, look at other's write-ups, discuss word for word how something should be proved, etc. Be sure to note with whom you collaborate if you do.
• Complete the problems on this worksheet.

Homework for class Friday, September 14:

• Review notes from class and work on expanding on the outline for the proof of part of Theorem 4: The Connections Theorem that we discussed in class. Can you see which facts, definitions and theorems we need to combine to fill in the details? Be ready to share your thoughts!
• Read Section 1.5 in your text (pages 43-47). Make flashcards! Write down questions to bring to class.
• Complete this worksheet on Section 1.5 and bring your work to class to discuss.
• Complete the Section 1.5 Practice Problems on page 47 of the text. This will not be collected, and you should check your answers on pages 49-50.

### WEEK 2: September 3 - September 7

Quiz 1 will take place on Monday at the beginning of class. It will cover Sections 1.1 and 1.2. Be prepared to state definitions and theorems, give examples with explanations, and complete short exercises.

Homework for class Monday, September 3:

• Practice material in Sections 1.1 and 1.2 with the first real WeBWorK assignment here. It isn't as long as it looks! But be very careful about how many attempts you have for each question!!! For many of these you only have ONE or TWO attempts! This is due Monday at 1:00pm.
• Complete this worksheet on Section 1.3 and bring your work to class to discuss. Also while you are reading, you are encouraged to take additional notes and record questions. You should also feel free to fill in the blanks for any skipped steps in the reading by working through calculations yourself!
• Complete these practice problems from Section 1.2 (pages 21-22): 1, 5, 11, 13, 15, 21, 23, 25. These will NOT be collected, but you should do ALL of these at least in your head if not on paper. In fact, you should do MORE odd problems if you are not confident after completing these! Note that AFTER you have solved these questions you can check your answers in the back of the textbook.

Homework for class Wednesday, September 5:

• Remember to bring in your picture if you forgot to bring it to your appointment!
• If you didn't have it ready for Monday, complete this worksheet on Section 1.3 and bring your work to class to discuss. Also while you are reading, you are encouraged to take additional notes and record questions. You should also feel free to fill in the blanks for any skipped steps in the reading by working through calculations yourself!
• Also complete this worksheet on Section 1.3 and bring your work to class to discuss. Also while you are reading, you are encouraged to take additional notes and record questions. You should also feel free to fill in the blanks for any skipped steps in the reading by working through calculations yourself!
• Complete the Practice Problems on page 32 of the text. This will not be collected, and you should check your answers on pages 34-35.
• Complete these practice problems from Section 1.2 (pages 21-22): 27, 29 and 31 (Draw what is happening geometrically here!). These will not be collected, but you should do ALL of these at least in your head if not on paper. In fact, you should do MORE odd problems if you are not confident after completing these! Note that AFTER you have solved these questions you can check your answers in the back of the textbook.

Collected Homework (Due Friday, September 7 at 1:55pm):

• Remember that although you may discuss this assignment with others, your write up should be your own. Do not share your write-up, look at other's write-ups, discuss word for word how something should be proved, etc. Be sure to note with whom you collaborate if you do.
• Complete the following problems:
1. Number 33 from Section 1.1, page 11. Show your work as was done for $T_1$ in the problem statement above the question.
2. Number 34 from Section 1.1, page 11. Use the hint!!! Remember to show each step separately!
3. Number 12 from Section 1.2, page 22. Be sure to show your work!
4. Number 20 from Section 1.2, page 22. Change the directions slightly to finding ALL possible $h$ and $k$ that fulfill the requirements for each part (not just one pair for each part). Be sure to show your work and explain your reasoning where appropriate! Don't forget to use Theorems in explanations!
5. For each of the following, decide whether or not it is possible for a system to satisfy the given description. If it is possible, give an augmented matrix (in row-echelon or reduced row-echelon form) that corresponds to such a system and prove that the corresponding system does in fact fulfill the requirements; if it is not possible, prove that it is not possible. (Hint: Theorems are helpful in proving!) (a) A system of 5 equations in 3 unknowns that has exactly 1 solution. (b) A system of 5 equations in 3 unknowns that has infinitely many solutions. (c) A system of 5 equations in 3 unknowns that has exactly 2 solutions.
6. Prove part (vii) of the Algebraic Properties of Vectors in $R^n$ Theorem (p. 27). See the solution to Practice Problem 1 of Section 1.3 for an example of how such a proof should go. Note that the sample proof on page 34 is really an outline for a proof. Be sure to include sentences and write your proof in paragraph form. You will quote definitions and properties of real numbers in your proof.

Homework for class Friday, September 7:

• Reread Section 1.3 in your text! Then complete any parts of the group work sheet we were working on in class that you did not finish. Bring your work to class to share and discuss.
• Try these practice problems from Section 1.3 (pages 32-33): 1, 5, 9, 11, 15, 21 and 25. These will not be collected, but you should do as many as you need to in order to feel comfortable with the material. In fact, you should do more odd problems if you are not confident after completing these! Note that AFTER you have solved these questions you can check your answers in the back of the textbook.
• Complete this worksheet on Section 1.4 and bring your work to class to discuss. Also while you are reading, you are encouraged to take additional notes and record questions. You should also feel free to fill in the blanks for any skipped steps in the reading by working through calculations yourself!
• Continue reading/reviewing the Book of Proof by Richard Hammack. For this week, read Chapter 4: Direct Proof. Pay special attention to Section 4.3 that starts on page 92 (page 6 of the pdf). The answers to the odd exercises are found in the Solutions section of the text. At a minimum, complete the exercises 3, 5 and 11 on page 100 (page 14 of the pdf), and as with all practice sets, do as many odd problems as you need to in order to feel comfortable with the material. You should be sure to work through this chapter by Wednesday. Note that there is a link to this text at the top of this page. I encourage you to ask me any questions you have on this material in office hours.

### WEEK 1: August 27 - August 31

Welcome to Linear Algebra!!!

Homework due Tuesday, August 28:

Although I will not normally assign homework to be due on non-class days, this week we will need to in order to get started and refresh our memories. Please complete the following:

Homework for class Wednesday, August 29:

• Read the syllabus! In fact, read it at least two times. You should be sure you have read all of it and understand what is expected. Please ask if you have questions. Note the paper copy I gave you is blue so that you can easily find it. Refer to it often. (There is also a link to the syllabus at the top of this page.)
• Put the exam dates from the syllabus on your calendar. Note that the midterm exams begin at 1:25, a half hour before our usual class time. Let me know ASAP if you have any issues with this.
• Although it is not required, it is recommended that you take MATH 135 before you take this course. If you have not yet taken MATH 135 or if you feel rusty, you should do additional outside reading on logic and proof writing as you will need those skills from time to time in this course. Although we will review a bit along the way, you will benefit highly from having a firm foundation on these concepts. There is a free online text, Book of Proof by Richard Hammack, that I recommend you review. For this first week, read Chapter 2: Logic. Pay special attention to Section 2.10 on Negation that starts on page 57 (page 25 of the pdf). The answers to the odd exercises are found in the Solutions section of the text. At a minimum, complete the odd exercises in Section 2.10 on pages 60-61 (pages 28-29 of the pdf). You should be sure to work through this chapter by Monday. Note that there is a link to this text at the top of this page.
• I put together a website for my MATH 135 classes to help with proof writing and presentations. Read the Proof Writing and Presentation Tips website. Use this as a reference when you are preparing your homework and presentations for class. Note there is a link to this site at the top of this web page as well.
• Read the Introduction to Chapter 1 and Section 1.1 in your text. This covers pages 1-9. We started discussing some of this in class.
• Complete this worksheet on Section 1.1 and bring your work to class to discuss. Also while you are reading, you are encouraged to take additional notes and record questions. You should also feel free to fill in the blanks for any skipped steps in the reading by working through calculations yourself!
• Complete this worksheet on Section 1.2 and bring your work to class to discuss. Also while you are reading, you are encouraged to take additional notes and record questions. You should also feel free to fill in the blanks for any skipped steps in the reading by working through calculations yourself!

Collected Homework (Due Friday, August 31 at 1:55pm):

• Remember that although you may discuss this assignment with others, your write up should be your own. Do not share your write-up, look at other's write-ups, discuss word for word how something should be proved, etc. Be sure to note with whom you collaborate if you do.
• Complete the problems on this worksheet.

Homework for class Friday, August 31: