Page 535 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition

Chapter 6

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 6.1

T1. (Weighted Euclidean Inner Products) See if you can program your utility so that it produces the value of a weighted
Euclidean inner product when the user enters n, the weights, and the vectors. Check your work by having the program do
some specific computations.

T2. (Inner Product on ) See if you can program your utility to produce the inner product in Example 7 when the user enters
the matrices U and V. Check your work by having the program do some specific computations.

T3. (Inner Product on ) If you are using a CAS or a technology utility that can do numerical integration, see if you can

program the utility to compute the inner product given in Example 9 when the user enters a, b, and the functions and

. Check your work by having the program do some specific calculations.

Section 6.3
T1. (Normalizing a Vector) See if you can create a program that will normalize a nonzero vector v in when the user enters v.

T2. (Gram–Schmidt Process) Read your documentation on performing the Gram–Schmidt process, and then use your utility to
perform the computations in Example 7.

T3. ( -decomposition) Read your documentation on performing the Gram–Schmidt process, and then use your utility to
perform the computations in Example 8.

Section 6.4

T1. (Least Squares) Read your documentation on finding least squares solutions of linear systems, and then use your utility to
find the least squares solution of the system in Example 1.

T2. (Orthogonal Projection onto a Subspace) Use the least squares capability of your technology utility to find the least