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Chapter 7: Q5E (page 380)

For the matrices A in Exercises 1 through 10 , determine whether the zero state is a stable equilibrant of the dynamical systemx鈫�(i+1)=Ax鈫�(i)

5.A=[0.50.6鈭�0.31.4],

Short Answer

Expert verified

Unstable

Step by step solution

01

Determine whether the zero state is a stable equilibrant

We solve

det(A鈭�位I)=0|0.5鈭�位0.6鈭�0.31.4鈭�位|=0(0.5鈭�位)(1.4鈭�位)+0.18=0位2鈭�1.9位+0.88=0位1,2=1.9卤3.61鈭�3.522=0.8,1.1

Since|位2|>=1 then the equilibrium is unstable

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Most popular questions from this chapter

Two interacting populations of coyotes and roadrunners can be modeled by the recursive equations

c(t + 1) = 0.75r(t)

r(t + 1) = 鈭�1.5c(t) + 2.25r(t).

For each of the initial populations given in parts (a) through (c), find closed formulas for c(t) and r(t).

(a)c(0)=100,r(0)=200(b)c(0)=r(0)=100(c)c(0)=500,r(0)=700

find an eigenbasis for the given matrice and diagonalize:

A=19[74-4418-481]

Representing the reflection about the planex-2y+2z=0.

Find all2脳2matrices for which[12]is an eigenvector with associated eigenvalue 5 .

Find an eigenbasis of given matrix and diagonalize it.

A=(1326)

True or false? If the determinant of a 2 脳 2 matrix A is negative, then A has two distinct real eigenvalues.
See all solutions

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