• In Strang, read Section 6.1, pages 274-283.
• In Strang, pages 283-287, do exercises #1, 2, 3, 4, 9, 11, 13, 15, 16, 17, 22, 25, 28, 29, and 33.

• In Strang, read Section 6.2, pages
• Do the exercises at the end of the activity Matlab and Coordinate Systems.

• Extra Credit Quiz #6 must be submitted no later than Wednesday, Dec. 6.

• Extra Credit Quiz #7 must be submitted no later than Friday, Dec. 8.

• Extra Credit Quiz #8 must be submitted no later than Friday, Dec. 8.

Fall 2005

Directions: Please follow these directions on all homework assignments.

1. On your homework assignment, place your name and assignment number in the top right corner of the page.
2. If an assignment takes more than a page, please staple the pages together.
3. Assignments will be handed in during classtime in separate piles: the assignment #1 pile, the assignment #2 pile, etc., so please do not staple two or more assignments together.
4. Simple one or two word answers or choices without explanatory prose are not acceptable. In all cases, use sound writing to justify your response.

• Assignment #1
  • Read the Syllabus
  • After logging onto Blackboard, update all your personal information. It is very important that your email address is current and correctly entered in Blackboard.
  • Once you've updated your personal information, read the welcome message on the Discussion Board and reply to the thread.
• Assignment #2
  • Download the ATLAST Matlab files at http://online.redwoods.edu/instruct/darnold/linalg/atlast65.zip. To install on your home machine, do the following:
    • On your home machine, create a directory called linear on your root drive.
    • Create a subdirectory named atlast65 in the linear directory and place the atlast.zip file downloaded from the link above into this subdirectory. Unzip the atlast.zip file.
    • Open Matlab and type pathtool at the Matlab prompt. Click the Add with Subfolders... button, then browse and select the linear directory. Click the Save and Close buttons, in that order.
    • To test your installation, type cogame at the Matlab prompt to start the coordinate game demonstrated in class. If you experience problems, cut and paste any error messages on the Discussion Board in Blackboard.
    • Spend a little time playing the cogame before doing your reading and assigned problems that follow.
  • Read Chapter 1, Section 1, in Strang, pages 1-7.
  • In Strang, pages 7-10, do exercises #1-3, 6, 13-19, 24, and 25.
• Assignment #3
  • Download the activity Matlab and Vectors and read the activity while seated at the computer, typing in all the example code as you read.
  • Once you've finished reading and executing the commands in the activity, do each of the exercises at the end of the activity.
  • To receive credit for your work, copy and paste the successful commands and output for each question into a Word document. Save the document to your home directory, then send it to the printer.
  • This assignment is due Friday.
• Assignment #4
  • Read Chapter 1, Section 2, in Strang, pages 10-17.
  • Pages 17-20, do exercises #1, 4, 5, 6bc, 7, 8, 10-13, 21, 25, 29, and 30.
• Assignment #5
  • In Strang, read Chapter 2, Section 1, pages 21-30.
  • If you are working at home, the programs sys23 and sys34 are contained in the archive linalg.zip. You may find this archive of files useful. Download and unzip the file linalg.zip to your harddrive, then open the pathtool in Matlab and add the directory to your path.
  • In Strang, pages 30-34, do exercises #1, 2, 5-7, 10, 11, 14, 16-18, 21-23, 30-32.
• Assignment #6
  • Download the activity Matlab and Matrices and read the activity while seated at the computer, typing in all the example code as you read.
  • Once you've finished reading and executing the commands in the activity, do each of the exercises at the end of the activity.
  • To receive credit for your work, copy and paste the successful commands and output for each question into a Word document. Save the document to your home directory, then send it to the printer.
  • This assignment is due Monday of next week before the end of the day.
• Assignment #7
  • In Strang, read Chapter 2, Section 2, pages 35-41.
  • In Strang, pages 41-45, do exercises #1, 2, 6-9, 11, 13, 18, 21-23.
• Assignment #8
  • Do the examples in Matlab and RREF while seated at the computer.
  • After completing the examples in Matlab and RREF, do each of the exercises at the end of the activity. In exercises #1-8, record the original system on your paper, then the reduced row echelon form of the system, then write your solution. In the case of Exercise #9, use the sys34 program and obtain printouts of the resulting plots.
• Assignment #9
  • In Strang, read Chapter 2, Section 3, pages 46-52.
  • In Strang, pages 53-56, do exercises #1, 3-5, 7, 12, 13, 21, 24-26, 28, 30. You may find the Matlab routine reduce.m helpful. This file is in the archive linalg.zip, so if you have previously downloaded and installed this archive, you will find that reduce.m is already set to go.
  • In Strang, page 54, do exercise #17. Once you obtain your solution, use Matlab to obtain a plot of your solution like this:

    x=[-1;2;5];
    y=[1;4;-6]
    A=[x.^2,x,ones(3,1)];
    format rat
    R=rref([A,y])
    a=-13/18;
    b=31/18;
    c=31/9;
    xx=linspace(-2,6);
    yy=a*xx.^2+b*xx+c;
    plot(xx,yy)
    line(x,y,'LineStyle','none','Marker','*')
    grid on
    t1=text(-1,1,'   (-1,1)')
    text(2,4,'   (2,4)', 'VerticalAlignment','bottom')
    text(5,-6,'(5,-6)   ','HorizontalAlignment','right')
    title(['The graph of p(x) = (', num2str(a),') x^2 + (', num2str(b), ') x + ', num2str(c), '.'])
    

• Assignment #10
  • Read the activity The Interpolating Polynomial while seated at the computer. Don't start the exercises until you've completed all the examples in the activity, typing in the commands as you go.
  • Do each of the exercises at the end of the activity for homework. This assigment is due next Monday.
• Assignment #11
  • In Strang, read Chapter 2, Section 4, pages 56-65.
  • In Strang, pages 65-68, do exercises #1, 2, 4, 6, 7, 9, 11, 14, 17, 19, 23-24. In the case of "true" or "false" problems, provide an abstract proof if the statement is "true," and a specific counterexample in the case that the statement is "false."
• Assignment #12
  • In Strang, pages 69-79, do exercises #26-31, and 33.
• Assignment #13
  • In Strang, read Section 2.5, pages 71-78.
  • In Strang, pages 78-82, do exercises #1, 2, 5, 6, 9, 10, 12,, 17, 25 ,26, 29, 32, 34, and 35.
• Assignment #14
  • Read the activity Numerical Linear Algebra while seated at the computer. Don't start the exercises until you've completed all the examples in the activity, typing in the commands as you go.
  • Do each of the exercises at the end of the activity for homework. This assigment is due next Monday.
• Assignment #15
  • In Strang, read Section 2.6, pages 83-90.
  • In Strang, pages 91-95, do exercises 7, 8, 11, 12, 13, 15, 16, 32, and 33.
• Assignment #16
  • In Strang, read Section 2.7, pages 96-104
  • In Strang, pages 104-108, do exercises #1, 2, 6, 7, 11, 12, 14, 16, 18, 19, 20, 22, and 34.
• Assignment #17
  • Read the activity Population Modeling Using the Leslie Matrix, Part 1 and answer the questions at the end of the activity. This assignment is due next Monday.
• Assignment #18
  • In Strang, read Section 3.1, pages 111-117
  • In Strang, pages 118-121, do exercises #2, 9, 10, 17, 18, 19, 22, and 24.
• Assignment #19
  • Complete the exercises at the end of the activity The Dimension of a Vector Space The assignment is due next Monday.
• Assignment #20
  • In Strang, read Section 3.2, pages 122-130.
  • In Strang, pages 130-133, do exercises #15, 19, 21, 23, 25, 26, 28, 30, and 31.
• Assignment #21
  • (Recommended) In Strang, read Section 3.3, pages 134-139.
• Assignment #22
  • In Strang, read Section 3.4, pages 144-152.
  • In Strang, pages 152-156, do exercises 1-6, 18, 19, 28-30.
• Assignment #23
  • In Strang, read Section 3.5, pages 157-167.
  • In Strang, pages 167-170, do exercises #1, 5, 7, 8, 9, 10, 16, 17, 20, 21, 24, and 25.
• Assignment #24
  • In Strang, read Section 3.6, pages 173-179.
  • In Strang, pages 180-182, do exercises #1, 2, 3, 4, 6, 11, 12, 14, 16, 21, 22, and 23.
• Assignment #25
  • In Strang, read Section 4.1, page 184-190.
  • Remark: It is not enough on your homework to simply fill in a blank and be content. For example, consider exercise #4 on page 191 of Strang. The correct statement is "If AB=0 then the columns of B are in the nullspace of A." However, if that is all you fill in on your homework, then you are cheating yourself of an opportunity to advance your ability in mathematics. Rather, it's time to provide a proof of that statement if you believe you have filled in the blank correctly. Thus, if AB=0, then
    
    0 = AB = A[b1, b2, ... , bn] = [Ab_1, Ab_2, ..., Ab_n]

    Of course, this means that each column of AB is the zero vector. That is,

    Ab_i = 0

    for all i = 1, 2, ... , n. This, in turn, implies that each b_i is in the nullspace of A for i = 1, 2, ... , n.

    This is the type of response that I expect when I look at your homework. Anything less is not in a place that all of us should be trying to reach.

  • In Strang, pages 191-193, do exercises #1, 3, 5, 12, 17, 25, and 26.
• Assignment #26
  • In Strang, read Section 4.2, pages 194-202.
  • In Strang, pages 202-204, do exercises #1, 3, 5, 6, 7, 8, 9, 11, 12, 17, 18, 19, 20, 21, and 22.
• Assignment #27
  • In Strang, read Section 4.3, pages 206-215.
  • Do exercises #4-10 at the end of the activity Least Squares.
• Assignment #28
  • In Strang, read Section 4.4, pages 219-228.
  • In Strang, do exercises #2, 4, 5, 10, 11, 13, 14, 21, 22, 23, 24, 33, and 34.
• Assignment #29
  • Do the exercises at the end of the activity Matlab and Coordinate Systems. The assignment is due next Monday.
• Assignment #30
  • In Strang, read Section 5.1, pages 233-240.
  • IN Strang, pages 240-244, do exercises #1, 3, 5, 7 (explain which and why one of these matrices is a "reflection" matrix), 8, 12, 14, 16, 17, 20, 22, 24, 28, and 29.
• Assignment #31
  • In Strang, read Section 5.2, pages 245-253.
  • In Strang, pages 253-256, do exercises #1, 4, 5, 15, 17, and 18.
• Assignment #32
  • In Strang, read Section 5.3, pages 259-260. If you are attempting the extra credit stuff from the MIT quiz, you might read more, but only pages 259-260 are necessary to complete the assigned problems that follow.
  • In Strang, pages 269-270, do exercises #1-3.
• Assignment #33
  • In Strang, read Section 6.1, pages 274-283.
  • In Strang, pages 283-287, do exercises #1, 2, 3, 4, 9, 11, 13, 15, 16, 17, 22, 25, 28, 29, and 33.
• Assignment #34
  • Read the activity Difference Equations while seated at the computer. Do each of the exercises at the end of the section.
  • In Strang, pages 269-270, do exercises #1-3.