Here are the Practice Problems and
Answers and the previous exams without the answers in case you want to retry some of them.
For Monday, 2 May:
Look for Postings about the final late on the Weekend or on Monday
- Back to our regular classroom.
- Review Wednesday's Handout about Stage Matrix Models. Note
the Homework due Monday.
- Read Friday's Handout about Stage Matrix Models.
- Read Sample Maple Code for Stage Matrix Models.
- Skim section 5.6 pages 301 to middle of 303, 307(Owls) to 309 in your text.
- Review Section 5.3 on Diagonalization.
For Friday, 29 April:
Meet in Lansing 310
- Read Wednesday's Handout about Stage Matrix Models. Note
the Homework due Monday.
Maple Code and choose "Save As"
and put the file in a location
where you can find it later. Then click on the file and Maple should open it.
On a Mac using the Firefox browser, Control-click on the file above and choose
"Save Link As..." and save the file to a location (Desktop) where you can find it.
It should have a Maple icon. Click on the icon and Maple should open it. (If you do this
in Safari, the file name may have the extension ".mw.xml". In this case click on the file
name once and remove ".xml".) You can save the file to your personal computer this
way, but you will need access to Maple to open it.
- Skim section 5.6 pages 301 to middle of 303, 307(Owls) to 309 in your text.
- Review Section 5.3 on Diagonalization.
For Wednesday, 27 April: Meet in Gulick 208A
- Friday's Handout with Assignment 19 due Wednesday.
- Monday's Handout which includes some
problems due next Monday.Read the Case Study on Owl populations (handout). We will conclude
the term with a study of stage-matrix models.
Skim section 5.6 pages 301 to middle of 303, 307(Owls) to 309 in your text.
- Northern Spotted Owl Handout.
- Review Section 5.3 on Diagonalization.
For Monday, 25 April
For Friday, 22 April
- Monday's Handout with Assignment 18
Markov Maple problems due Friday (work with a partner, see code below).
- Maple code for Example 2 in the notes above.
- Wednesday's Handout with practice for eigenvectors.
due Wednesday. Markov Maple problems due Friday (work with a partner, see code below).
- Work on
WeBWorK SHW13 on Eigenvectors. Due Monday night.
- Review Section 5.1 on Eigenvalues.
- Read Section 5.2 on the Characteristic Equation.
For Wednesday, 20 April
- Monday's Handout with Assignment 18. Rank problems
due Wednesday. Markov Maple problems due Friday (work with a partner, see code below).
- Maple code for Example 2 in the notes above.
- Read/Review Section 4.9 on Markov Chains.
- Read Section 5.1 on Eigenvalues.
For Monday, 18 April
For Friday, 15 April
For Wednesday, 13 April
For Monday, 11 April
- Friday's Handout with assignment and practice problems
due Wednesday.
- Work on
WeBWorK LHW10. Due Sunday at Midnight. (4 Problems)
- Work on
WeBWorK LHW11. Due Tuesday at Midnight. (10 Problems)
- Read/Review Section 4.4 on Coordinates.
- Read Section 4.5 on Dimension.
For Friday, 8 April
- Wednesday's Handout with assignment and practice problems
due Friday and the Basis Handout.
- Work on
WeBWorK LHW10. Due Sunday at Midnight. (4 Problems)
- Work on
WeBWorK LHW11. Due Tuesday at Midnight. (10 Problems)
- Review Friday's notes on Transformations. We did more than in the text.
- Read/Review Section 4.3 on Bases.
- Review Classnotes on Linear Transformations.
For Wednesday, 6 April
For Monday, 4 April
For Friday, 1 April
- Wednesday's Handout with assignments
including problems due Friday. More problems will be added to the Monday assignment.
- 3-Minute Quiz on Friday: See the Handout above.
- Work on
WeBWorK Subspaces. Due Tuesday.
- Review Section 4.2 on the Null and Column Space and on Kernel and Range of
a Linear Transformation. This material is more abstract. See the handout for
Practice Problem suggestions. Read Section 4.3 on Bases.
For Wednesday, 30 March
- Monday's Handout with assignments.
More problems will be added to the Friday assignment.
- Read Section 4.2 on the Null and Column Space and on Kernel and Range of
a Linear Transformation. This material is more abstract. Try page 205 Practice Problems
#1 and 2 (the answers are on page 207). Then try page 205-206 #1, 3, 7.
For Monday, 28 March
- Friday's Handout with future assignments. Likely
due Wednesday and Friday.
- Read Section 4.1 on Vector Spaces and Subspaces. This material is more abstract.
Next time we will discuss subspaces (see pp. 193--195). Try pages 195--196 #1-4
(these are about closure) and 25-30. After reading about subspaces try #5, 7, 9, 11.
Check the answers in the back of the text.
For Friday, 25 March
- Due Friday: Assignment 14A pages of 3 and 4 from Wednesday's
Handout
.
- Read Section 4.1 on Vector Spaces and Subspaces. This material is more abstract.
Next time we will discuss subspaces (see pp. 193--195). Try pages 195--196 #1-4
(these are about closure) and 25-30. After reading about subspaces try #5, 7, 9, 11.
Check the answers in the back of the text.
For Wednesday, 23 March
- Complete Assignment 13 due Wednesday.
- Review Monday's Handout. In particular
Read Section 3.3 (we will not cover Cramer's Rule).
- Read Section 4.1 on Vector Spaces and Subspaces. This material is more abstract.
Close reading exercises (Answers in back of text): Try Practice Problem #1 on
page 195 and then try Exercises #1, 3 on the same page.
For Monday, 21 March
- Work on Assignment 13 due Wednesday.
- Read Section 4.1 on Vector Spaces and Subspaces. This material is more abstract.
Close reading exercises (Answers in back of text): Try Practice Problem #1 on
page 195 and then try Exercise #1 on the same page.
For Thursday, 10 March
For Wednesday, 9 March:
- Finish
Determinants 2. A
more
in-depth look at determinant calculations. Due Thursday Night.
- Do Assignment 12 from Monday's Handout. Due Wednesday.
For Monday, 7 March:
- Do
Determinants 1. A few
problems on determinant calculations. Due Monday Night.
- Start
Determinants 2. A
more
in-depth look at determinant calculations. Due Thursday Night.
- Finish Assignment 11. Additional problems
on determinants were added Friday.
- Friday's Handout with Connections
Theorem and the Dictionaries. Also suggested practice and a Review Problem.
For Thursday-Friday, 3-4 March:
For Wednesday, 2 March:
For Monday, 29 February:
For Friday, 26 February:
For Wednesday, 24 February:
- Monday's Handout with one problem due Wednesday.
- WeBWorK HW4: Due Thursday.
Seven problems on linear transformations.
- Start Assignment 9 that will be due Friday.
- On Wednesday, Feb 24th: Math candidate talk at 4:30pm in Napier 201 (Snacks at 4:15pm).
Dr. Jocelyn Bell. Remember: Attendance at two
talks is required.
- Review Section 2.1. Matrix operations. Reading Check (not to be handed in, check answers
in back of text): Page 100: #1, 3.
- Review Section 2.1. Matrix operations. Reading Check (not to be handed in, check answers
in back of text): Page 100: #5, 7, 8, 9, 10, 23, 25(this is a great problem!), 31.
For Monday, 22 February:
- Finish Assignment 8 that will be due Monday.
- WeBWorK HW4: Due Saturday.
Problems on linear transformations.
Friday's Handout-First Few Problems of Assignment 9.
This includes some problems for Next Friday's Hand In.Read 1.10 (Applications) Pages 80 to the top of 82. This is the background for a Homework problem.
- Read Section 2.1. Matrix operations. Reading Check (not to be handed in, check answers
in back of text): Page 100: #1, 3.
For Friday, 19 February:
- Work on Assignment 8 that will be due Monday.
- WeBWorK HW4: Due Saturday.
Problems on linear transformations.
- On Friday, Feb 19th: Math candidate talk at 4:30pm in Napier 201 (Snacks at 4:15pm).
Dr. Eric Bucher. Remember: Attendance at two
talks is required.
- Read/Review Section 1.9.
Key Ideas: one-to-one transformation and onto transformations and their equivalents.
- Reading Check (not to be handed in, check answers
in back of text): Page 79: #25, 27, 29, 31, 35.
- Read 1.10 (Applications) Pages 80 to the top of 82. This is the background for a Homework problem.
- Read Section 2.1. Matrix operations. Reading Check (not to be handed in, check answers
in back of text): Page 100: #1, 3.
For Wednesday, 17 February:
- Due Wednesday, 17 February: Assignment 7. A quick check on
transformations.
- WeBWorK HW4:
Problems on linear transformations.
- Monday's Handout.
- Read/Review Section 1.9.
Key Ideas:
Linear Transformations are Matrix Transformations (Theorem 10), standard matrix of a
linear transformation, one-to-one transformation, onto transformation.
- Reading Check (not to be handed in, check answers
in back of text): Page 78: #1, 3 (see p 73-4), 9 (see p 73-4), 17, and 19. All of these are indirectly
practice for the exam. After reading closely, try the T/F in #21.
For Monday, 15 February
- Due Monday, 15 February: Exam Monday Evening at 6:00-8:00pm in Gulick 206A.
- WeBWorK HW3:
Problems on linear independence.
- Definitions, Facts, and Theorems for Test 1.
- Friday's Handout.
- Read/Review Section 1.8. Then start Section 1.9.
Key Ideas: Transformation, Linear Transformation, Properties of Linear Transformations (see page 66, (3), (4), (5)),
Linear Transformations are Matrix Transformations (Theorem 10),
and standard matrix of a linear transformation.
- Reading Check (not to be handed in, check answers
in back of text): Page 68: #1 3, 5, 7, 9, 15, and 17. All of these are indirectly
practice for the exam. After reading closely, try the T/F in #21.
- Answers to previous assignments:
- Answers to Assignment 6, Part 2.
- Answers to Assignment 6, Part 1.
- Answers to Assignment 5.
- Answers to Assignment 4.
- Answers to Assignment 3.
- Answers to Assignment 2.
- Answers to Assignment 1.
For Friday, 12 February:
- Due Friday, 12 February: Assignment 6, Part 2.
WeBWorK HW3 will open
on Tuesday. Due Monday, February 15th. These are problems on linear independence.
- Facts and Theorems for Test 1. I will add some
definitions to this list.
- On Thursday, Feb 11th: Math candidate talk at 4:30pm in Napier 201 (Snacks at 4:15pm).
Dr. Alexander Diaz Lopez. Remember: Attendance at two
talks is required.
- Read Section 1.7. Memorize the definition of linear independence. We will use this
notion repeatedly. Reading Check (not to be handed in, check answers
in back of text):
Basics: Page 60-61: \#1, 3(by inspection), 5, 7(by inspection), 9 (nice), 11,
15, 17 ,19, 21, 33, 35.
- Read Section 1.8. Linear Transformations
For Wednesday, 10 February:
- Due Wednesday, 10 February: Assignment 6, Part 1.
Additional problems will be assigned for Friday.
WeBWorK HW3 will open
on Tuesday. Due Monday, February 15th. These are problems on linear independence.
- Day 9 (Monday's) Handout.
- On Thursday, Feb 11th: Math candidate talk at 4:30pm in Napier 201 (Snacks at 4:15pm).
Dr. Alexander Diaz Lopez. Remember: Attendance at two
talks is required.
- Review Section 1.5. See previously assigned practice.
- Read Section 1.7. Memorize the definition of linear independence. We will use this
notion repeatedly. Reading Check (not to be handed in, check answers
in back of text): Section 1.7: Practice: Page 60 #1-4 (answers on page 62).
Basics: Page 60-61: \#1, 3(by inspection), 5, 7(by inspection), 9 (nice), and 11.
For Monday, February 8: If the focus last week was on the
span of a set of vectors, this
week the key notion is
linear independence.
- Due Monday, 8 February: Final Version Assignment 5
- On Monday, Feb 8th: Math candidate talk at 4:30pm in Napier 201 (Snacks at 4:15pm).
Dr. Caitlyn Parmelee from University of Nebraska-Lincoln.
Title: Title: Modeling in Mathematical Neuroscience . Remember: Attendance at two
talks is required.
- Review Section 1.5. Reading Check (not to be handed in, check answers
in back of text): Section 1.5: #1, 5. Then try #9, 11 (see Examples 1 and 2).
The next few problems are just slightly ahead of where we are in class (Read page 45).
Section 1.5: #15, 17, and 19.
- Read Section 1.7. Memorize the definition of linear independence. We will use this
notion repeatedly.
Week 3
This week we introduce matrix-vector multiplication. We will find that we can express
a system of linear equations as a vector equation or as a matrix product. Each method
has its advantages.
This week we introduce a second way (and actually the more common way) matrix-vector
multiplication.
For Friday, February 5:
- Finish
WeBWorK HW2
due Thursday, 4 February.
- Due Monday, 8 February: Second Version Assignment 5 (more problems to
be added).
- On Friday, Feb 5th: Math candidate talk at 4:00pm in Napier 201 (Snacks at 3:45pm).
Dr. Saul Blanco-Rodriguez from Indiana University.
Title: Mathematics of Combinatorial (and other) Games. Remember: Attendance at two
talks is required.
- Section 1.4: #29 (Hint: First write the matrix in echelon form
and then perform row operations on it to take it out of echelon form!), 31, 33, and 35.
All of these would be good test questions. Also see the suggested practice from Wednesday.
- Read Section 1.5. Reading Check (not to be handed in, check answers
in back of text): Section 1.5: #1, 5. Then try #9, 11 (see Examples 1 and 2).
For Wednesday, February 3:
- Quiz on Wednesday: See the Day 6 Handout.
- Work on this WW set that is Due Thursday, 4 February:
WeBWorK HW2
- Due Monday, 8 February: First Version Assignment 5 (more problems to
be added).
- Review Section 1.4. Practice (not to be handed in, check answers
in back of text): Section 1.4: #1, 5, 9, 11, 15, 21, 23, 25.
- Still in Section 1.4: #29 (Hint: First write the matrix in echelon form
and then perform row operations on it to take it out of echelon form!), 31, 33.
All of these would be good test questions.
- Read Section 1.5. Reading Check (not to be handed in, check answers
in back of text): Section 1.5: #1, 5.
Week 2
We begin this week by proving a fundamental theorem about linear systems. Next we introduce
vectors and vector equations.
Key concepts this week include scalar mutiple of a vector,
linear combination of a set of vectors, span of a set of vectors, and
Rn. Review: Make sure you know how to use the Row Reduction Algorithm to
efficiently solve linear systems. Practice a few more.
For Monday, February 1:
- Due Monday, 1 February: Final Version Assignment 4
- Review Section 1.3. Practice (not to be handed in, check answers
in back of text): Section 1.3: #1, 5, 9, 11, 15, 21, 25.
- Read Section 1.4. Practice (not to be handed in, check answers
in back of text): Section 1.4: #1, 3.
For Friday, January 29:
For Wednesday, January 27:
Week 1
We will begin the course with a discussion of systems of linear equations and their solutions.
You should read at least
the first two sections of Chapter 1. Though this material is relatively easy, it requires care.
Make sure you understand the process of row reduction and row equivalence because these ideas will
be used repeatedly throughout the term. From the reduced row echelon form of an augmented matrix
you should be able to determine whether a system of equations has infinitely many, exactly one, or
no solutions. (You should be able to define any terms in boldface.)
Maple Resources
- Using Maple for Linear Algebra part 1: Matrix entry. YouTube
Video. This is an excellent video targeted for new users. It is
very helpful. Have the Maple software open when you start the video so you can follow
along, pausing the video as needed.
- Using Maple for Linear Algebra screencast 2. YouTube
Video. The second part of the video above.
- Another Introductory YouTube Maple Tutorial
for Linear Algebra Video. This one is not as polished as the first two, but does illustrate
some useful Maple tools not covered in the videos above (context menus and Tool menus).
- To download Maple Primer 1 first go to a campus networked computer (e.g., in Gulick or the Library).
On a Windows machine right-click on
MaplePrimer1.mw and choose "Save As" and put the file in a location
where you can find it later. Then click on the file and Maple should open it.
On a Mac using the Firefox browser, Control-click on the file above and choose
"Save Link As..." and save the file to a location (Desktop) where you can find it.
It should have a Maple icon. Click on the icon and Maple should open it. (If you do this
in Safari, the file name may have the extension ".mw.xml". In this case click on the file
name once and remove ".xml".)
- MaplePrimer1.pdf, a pdf version of the MaplePrimer1.mw file for reference.
- MaplePrimer2.mw. See the instructions for downloading MaplePrimer1.mw above.
- MaplePrimer2.pdf, a pdf version of the MaplePrimer2.mw file for reference.
- Maple Quick Start Video.
40 Minutes long, but you might want to watch the beginning. You should have Maple open so you can try commands as
they are described in the video. The video does not cover much linear algebra, but
you will see lots of things you can apply to calculus.
- Maple
Quick Start PDF. 29 pages. A quick intro to Maple that goes along with the video above.
