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Chapter 2
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 2.1
T1. (Determinants) Read your documentation on how to compute determinants, and then compute several determinants.
T2. (Minors, Cofactors, and Adjoints) Technology utilities vary widely in their treatment of minors, cofactors, and adjoints.
For example, some utilities have commands for computing minors but not cofactors, and some provide direct commands for
finding adjoints, whereas others do not. Thus, depending on your utility, you may have to piece together commands or do
some sign adjustment by hand to find cofactors and adjoints. Read your documentation, and then find the adjoint of the matrix
A in Example 6.
Use Cramer's rule to find a polynomial of degree 3 that passes through the points (0, 1), , , and (3, 7). Verify
T3. your results by plotting the points and the curve on one graph.
Section 2.2
T1. (Determinant of a Transpose) Confirm part (b) of Theorem 2.2.3 using some matrices of your choice.
Section 2.3
T1. (Determinant of a Product) Confirm Theorem 2.3.4 for some matrices of your choice.
T2. (Determinant of an Inverse) Confirm Theorem 2.3.5 for some matrices of your choice.
T3. (Characteristic Equation) If you are working with a CAS, use it to find the characteristic equation of the matrix A in
Example 6. Also, read your documentation on how to solve equations, and then solve the equation for the
eigenvalues of .
Section 2.4
T1. (Determinant Formulas) If you are working with a CAS, use it to confirm the formulas in Example 7. Also, use it to obta
