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Chapter 10
Technology Exercises
The following exercises are designed to be solved using a technology utility. Typically, this will be MATLAB, Mathematica, Maple,
Derive, or Mathcad, but it may also be some other type of linear algebra software or a scientific calculator with some linear algebra
capabilities. For each exercise you will need to read the relevant documentation for the particular utility you are using. The goal of
these exercises is to provide you with a basic proficiency with your technology utility. Once you have mastered the techniques in
these exercises, you will be able to use your technology utility to solve many of the problems in the regular exercise sets.
Sections 10.1 and 10.2
T1. (Complex Numbers and Numerical Operations) Read your documentation on entering and displaying complex numbers
and for performing the basic arithmetic operations of addition, subtraction, multiplication, and division. Experiment with
numbers of your own choosing until you feel you have mastered the operations.
T2. (Matrices with Complex Entries) For most technology utilities the procedures for adding, subtracting, multiplying, and
inverting matrices with complex entries are the same as for matrices with real entries. Experiment with these operations on
some matrices of your own choosing, and then try using your utility to solve some of the exercises in Sections 10.1 and 10.2.
T3. (Complex Conjugate) Read your documentation on finding the conjugate of a complex number, and then use your utility to
perform the computations in Example 1 of Section 10.2.
Section 10.3
T1. (Modulus and Argument) Read your documentation on finding the modulus and argument of a complex number, and then
use your utility to perform the computations in Example 1.
Section 10.6
T1. (Conjugate Transpose) Read your documentation on finding the conjugate transpose of a matrix with complex entries, and
then use your utility to perform the computations in Examples Example 1 and Example 3.
T2. (Unitary Diagonalization) Use your technology utility to diagonalize the matrix in Example 5 and to find a matrix that
unitarily diagonalizes . (See Technology Exercise T1 of Section 7.2.)
Copyright © 2005 John Wiley & Sons, Inc. All rights reserved.
