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Chapter 3
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.
Section 3.1
T1. (Vectors) Read your documentation on how to enter vectors and how to add, subtract, and multiply them by scalars. Then
perform the computations in Example 1.
T2. (DrawingVectors) If you are using a technology utility that can draw line segments in two or three-dimensional space, try
drawing some line segments with initial and terminal points of your choice. You may also want to see if your utility allows
you to create arrowheads, in which case you can make your line segments look like geometric vectors.
Section 3.3
T1. (Dot Product and Norm) Some technology utilities provide commands for calculating dot products and norms, whereas .
others provide only a command for the dot product. In the latter case, norms can be computed from the formula
Read your documentation on how to find dot products (and norms, if available), and then perform the computations in
Example 2.
T2. (Projections) See if you can program your utility to calculate when the user enters the vectors a and u. Check your
work by having your program perform the computations in Example 6.
Section 3.4
T1. (Cross Product) Read your documentation on how to find cross products, and then perform the computation in Example 1.
T2. (Cross Product Formula) If you are working with a CAS, use it to confirm Formula 1.
T3. (Cross Product Properties) If you are working with a CAS, use it to prove the results in Theorem 3.4.1.
