Math 224 Homework

Homework Assignments


  1. Due Tuesday, September 4.

    Section Suggested problems Problems to be turned in
    1.1 3, 11, 21, 25, 33, 37, 39 8, 26, 28, 36
    1.2 3, 11, 13, 33, 37, 40 4, 8, 30, 44
    1.3 (feel free to use Maple!) 1, 3, 7, 17, 19, 21, 29, 35 8, 12, 20, 30, 32, 38, 40a, 42, 46
    1.4 1, 13, 15 2(a), 4(a), 14


    Note: The assignment has been updated on August 29: in section 1.3, you are NOT required to turn in part (b) of Problem 40. If, however, you have already done both parts of problem 40, have seen induction previously, or are motivated to read Appendix A on induction, feel free to turn in both parts of problem 40! The assignment has been updated again on August 30: I changed the problems from section 1.4 to reflect what we have covered in class so far. Feel free to use Maple for the problems in section 1.3, but NOT for the problems in section 1.4.

    2. Homework 1 solutions as a .pdf file

  2. Due Tuesday, September 11.

    Section Suggested problems Problems to be turned in
    1.4 3, 21, 25, 29, 39, 41, 6, 14, 18, 22, 24, 28, 34, 42, 44, 46, 56
    1.5 1(a), 3(a), 13, 17, 21, 23 8(a), 14, 18, 26, 30, 35(a)
    Adjacency matrices and graph theory problem.


    For the Adjacency matrices and graph theory problem, please turn in (either write down or print out your Maple code) your adjacency matrix and the first few powers of the adjacency matrix. Try to determine how to interpret A^2, A^3, etc. in terms of the graph.

    Note: Unless specifically stated otherwise, feel free to use Maple for all of the problems in this and future assignments. On this assignment, please do 1.4# 14 and 1.4 #18 by hand (i.e. row-reduce by hand to row-echelon form and then use back substitution to solve the linear system). For all other problems, you are free (and in fact encouraged) to use Maple.

    Homework 2 solutions as a .pdf file



  3. Due Tuesday, September 18.

    Section Problems to be turned in
    1.6 4, 8, 10, 12, 18, 26, 32
    Additional Problem
    2.12, 4, 10, 12, 22, 26, 32


    Homework 3 solutions as a .pdf file

    Solution to the additional problem as a .pdf file

  4. Due Tuesday, September 25.

    Section Problems to be turned in
    2.2 4, 6, 8, 10
    2.34, 8, 10, 16, 19, 20, 24, 30


    Homework 4 solutions as a .pdf file



  5. Due Thursday, October 11.

    Section Problems to be turned in
    4.1 4, 8, 10, 12, 18, 22, 30, 38, 46, 50, 54
    4.28, 16, 18, 20, 24, 28, 32


    Note: No Maple is allowed for this homework assignment. You must compute all determinants by hand, and show your work!

    Homework 5 solutions as a .pdf file



  6. Due Tuesday, October 16.

    Section Problems to be turned in
    4.4 2, 8, 12, 14, 18, 26, 32
    5.1 45, 46. Use Maple (as in class) to solve these problems.


    Homework 6 solutions as a .pdf file



  7. Due Tuesday, October 23.

    Section Problems to be turned in
    5.1 2, 14, 22, 27, 28, 29, 30, 32, 38, 39


    Homework 7 solutions as a .pdf file



  8. Due Tuesday, October 30. Note: these problems will be checked for completion, but NOT for accuracy. You should self-check your homework for accuracy using the posted solutions, and use your homework to study for Test 2 (on Thursday, November 1, 2007).

    Section Problems to be turned in
    5.2 2, 6, 10, 12, 14, 15, 17
    5.3 10, 12


    Homework 8 solutions as a .pdf file



  9. Due Tuesday, November 13.

    Section Problems to be turned in
    6.1 8, 9, 11, 15, 17, 20, 25
    6.2 4, 8, 19, 20 (see Example 7 on p. 346 for help with #20)
    Note: For now (meaning for this assignment), I would like you to implement the Gram-Schmidt process by hand. Of course, you can use Maple to CHECK your work. For future assignments, you are free to use the GramSchmidt command in Maple to find orthogonal and orthonormal bases.

    Homework 9 solutions as a .pdf file



  10. Due Tuesday, November 27.

    Section Problems to be turned in
    6.3 2, 20, 21, 22, 23, 24, 31
    6.4 2, 8, 16, 21


    Homework 10 solutions as a .pdf file



  11. Due Tuesday, December 4. Note: these problems will be checked for completion, but NOT for accuracy. You should self-check your homework for accuracy using the posted solutions, and use your homework to study for Test 3 (on Thursday, November 6, 2007).

    Section Problems
    3.1 In-class worksheet on vector spaces. We finished the worksheet in class; just make sure that you understand why each set is or is not a vector space.
    3.2 2, 3, 4, 5, 8, 12, 13, 14, 18, 20
    3.3 4, 6, 8, 12, 21


    Homework 11 solutions as a .pdf file



  12. These problems will not be collected or graded, but there will be questions from Section 3.4 on the final exam, so you should make sure that you know how to do them.

    Section Problems
    3.4 22, 24, 27, 31, 32


    Homework 12 solutions as a .pdf file





About homework


Homework to be graded will be collected once per week, typically on Tuesdays. It serves as your opportunity to make sure that you can not only solve the problems, but also explain your solutions carefully, as this is the only way to be sure that you understand the underlying concepts. It is your job to explain your solution to the reader, not the reader's job to search for a right idea buried in what you have written. Although you are encouraged to work with other students on homework problems, you must write up your final solutions on your own, as the homework is intended to be preparation for the quizzes and exams. Homework may involve computer exercises as well as hand-written and computer explanation. Homework should be legible with explanations written in complete sentences. Illegible homework will not be read or graded. Homework must be turned in by the beginning of class on the given due date. No late homework will be accepted. If you know that you will be missing class, you must turn in your homework before you leave. Extensions may be granted for extenuating circumstances, but these must be discussed with me as early as possible.

In addition to the homework that will be graded and collected, I will often suggest additional problems for you to work on, especially in the beginning of the semester when a significant amount of drill work is necessary to master the new definitions and concepts. Although this homework will not be graded or collected, I strongly encourage you to solve the suggested problems. You should not worry about formally writing up solutions to the suggested problems; rather, just make sure that you are able to solve them and that you understand the underlying concepts. Note that you should also be reading the textbook sections as you do the homework--the examples are a great help.

Please feel free to ask questions about any problems (assigned or otherwise). I am always happy to help.

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