The Nature of Mathematics, 12th Edition
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Section 16.4 Homework Hints

    Problems 1-8
    These problems are testing your understanding of the key concepts in this section. Read the text and then paraphrase or describe each word or process in your own words. If you get stuck, look in the book, but don't copy your answers directly out of the book.
    Problems 9-16
    See Examples 1-3; don't forget the correct order of operations.
    Problems 17-18
    Carry out the matrix multiplication as shown in Example 4.
    Problems 19-20
    Show the product of [A][B] as well as [B][A]. Both of these products must be the inverse matrix, as shown in Example 6.
    Problems 21-22
    First, find the inverse as shown in Examples 7 and 9.
    Problems 23-26
    Write the augmented matrix and make the left-hand side look like the corresponding identity matrix.  See Example 10.
    Problems 27-32
    Start with the inverse from Problem 21. If you did not work Problem 21, you should do so now. Then, use this inverse to solve each system by first writing [A][X] = [B]. Finally, proceed as you did in Problems 17 and 18.
    Problems 33-38
    Start with the inverse from Problem 22. If you did not work Problem 22, you should do so now. Then, use this inverse to solve each system by first writing [A][X] = [B]. Finally, proceed as you did in Problems 17 and 18.
    Problems 39-44
    First find the inverse of the matrix of coefficients.
    Then, use this inverse to solve each system by first writing [A][X] = [B].
    Finally, proceed as you did in Problems 17 and 18.
    Problems 45-50
    Start with the inverse from Problem 23. If you did not work Problem 23, you should do so now. Then, use this iverse to solve each system by first writing [A][X] = [B]. Finally, proceed as shown in Example 12.
    Problems 51-54
    Start with the inverse from Problem 24. If you did not work Problem 24, you should do so now. Then, use this inverse to solve each system by first writing [A][X] = [B]. Finally, proceed as shown in Example 12.

    Note: Homework Hints are given only for the Level 1 and Level 2 problems.

    However, as you go through the book be sure you look at all the examples in the text. If you need hints for the Level 3 problems, check some sources for help on the internet (see the LINKS for that particular section. As a last resort, you can call the author at (707) 829-0606.

    On the other hand, the problems designated "Problem Solving" generally require techniques that do not have textbook examples.

    There are many sources for homework help on the internet.

    Algebra.help
    Here is a site where technology meets mathematics. You can search a particular topic or choose lessons, calculators, worksheets for extra practice or other resources.
    http://www.algebrahelp.com/

    Ask Dr. Math
    Dr. Math is a registered trademark. This is an excellent site at which you can search to see if your question has been previously asked, or you can send your question directly to Dr. Math to receive an answer.
    http://mathforum.org/dr/math/
    Quick Math
    This site provides online graphing calculators. This is especially useful if you do not have your own calculator.
    http://www.quickmath.com/

    The Math Forum @ Drexel
    This site provides an internet mathematics library that can help if you need extra help. For additional homework help at this site, click one of the links in the right-hand column.
    http://mathforum.org/

    Mathematics Home Page
    Access the Clemens and Alcuins Library of CSB/SJU and find one of the world's best collections of mathematical internet sites.
    http://library.csbsju.edu/rqs.phtml?subject_id=32

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