Math 404 Homework 3 - Spring 1998

Due February 11, 1998

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  • Problems in text are from
    John H. Matthews, Numerical Methods for Mathematics, Science, and Engineering, 2nd edition, Prentice Hall, 1992.

    Covers material from Chapter 3, Sections 3.5-3.7, and Chapter 4, Sections 4.1-4.3.

    1. Write a computer program that finds the inverse of an nxn matrix by using either the Gauss elimination-with-pivoting method or the LUP method. Test it by finding the inverse of the matrix 

       (  2  1  1  1   )
   (  3  2  1  0   )
   (  3  3  1  4   )
   (  2  2  1  4   )
    Multiply the inverse by the original matrix and find the sum of the absolute values of the difference between the matrix product and the 4x4 identity matrix. (Hint: If you use Gauss elimination and pivoting, consider swapping rows physically in memory rather than using row indices, since at the end you will want the rows of the augmented matrix in their proper order.)

    2. Section 3.6, p177: Exercise 9.

    3. Section 3.7, p188: Exercise 8.

    4. Section 4.1, p204: Exercises 5, 19.

    5. Section 4.2, p213: Exercise 4abcd. (Hint: It may be easier to do the 4 parts in the order dabc. You may want to use a matrix-equation-solver or matrix-inversion subroutine that you have set aside from some other program for part~d.)

    6. Section 4.3, p225: Exercise 3, 12ab.

    Last modified February 3, 1998

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