Page 672 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition
P. 672
If the coefficient matrix A of the system in 4 is diagonalizable, then the
general solution of the system can be expressed as
where , , …, are the eigenvalues of A, and is an
eigenvector of A corresponding to .
Prove this result by tracing through the four-step procedure discussed in the section
with
Consider the system of differential equations where A is a matrix. For what
11. values of , , , do the component solutions , tend to zero as
? In particular, what must be true about the determinant and the trace of A for this to happen?
Solve the nondiagonalizable system ,.
12.
Use diagonalization to solve the system , by first
13. writing it in the form . Note the presence of a forcing function in each equation.
Use diagonalization to solve the system , by first
14. writing it in the form . Note the presence of a forcing function in each equation.
Copyright © 2005 John Wiley & Sons, Inc. All rights reserved.
