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Chapter 9
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 9.1
T1.
(a) Find a general solution of the system
by computing appropriate eigenvalues and eigenvectors. .
(b) Find the solution that satisfies the initial conditions , ,
The electrical circuit in the accompanying figure, called a parallel LRC circuit, contains a resistor with resistance R ohms
T2. (Ω), an inductor with inductance L henries (H), and a capacitor with capacitance C farads (F). It is shown in electrical circuit
theory that the current I in amperes (A) through the inductor and the voltage drop V in volts (V) across the capacitor satisfy
the system of differential equations
where the derivatives are with respect to the time t . Find I and V as functions of t if , , , and the
initial values of V and I are V and .
Figure Ex-T2
Section 9.3
T1. (Least Squares Straight Line Fit)
