Page 124 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition

Chapter 1

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 1.1

T1. Numbers and Numerical Operations Read your documentation on entering and displaying numbers and performing the
basic arithmetic operations of addition, subtraction, multiplication, division, raising numbers to powers, and extraction of
roots. Determine how to control the number of digits in the screen display of a decimal number. If you are using a CAS, in
which case you can compute with exact numbers rather than decimal approximations, then learn how to enter such numbers
as , , and exactly and convert them to decimal form. Experiment with numbers of your own choosing until you feel you
have mastered the procedures and operations.

Section 1.2

T1. Matrices and Reduced Row-Echelon Form Read your documentation on how to enter matrices and how to find the
reduced row-echelon form of a matrix. Then use your utility to find the reduced row-echelon form of the augmented matrix in
Example 4 of Section 1.2.

T2. Linear Systems With a Unique Solution Read your documentation on how to solve a linear system, and then use your
utility to solve the linear system in Example 3 of Section 1.1. Also, solve the system by reducing the augmented matrix to
reduced row-echelon form.

T3. Linear Systems With Infinitely Many Solutions Technology utilities vary on how they handle linear systems with infinitely
many solutions. See how your utility handles the system in Example 4 of Section 1.2.

T4. Inconsistent Linear Systems Technology utilities will often successfully identify inconsistent linear systems, but they can
sometimes be fooled into reporting an inconsistent system as consistent, or vice versa. This typically happens when some of
the numbers that occur in the computations are so small that roundoff error makes it difficult for the utility to determine
whether or not they are equal to zero. Create some inconsistent linear systems and see how your utility handles them.

A polynomial whose graph passes through a given set of points is called an interpolating polynomial for those points. Some
T5. technology utilities have specific commands for finding interpolating polynomials. If your utility has this capability, read the

documentation and then use this feature to solve Exercise 25 of Section 1.2.

Section 1.3