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Chapter 9: Q19E (page 439)

True or False? If the trace and the determinant of a 3脳3matrix A are both negative, then the origin is a stable equilibrium solution of the systemdx鈫�dt=Ax鈫�. Justify your answer.

Short Answer

Expert verified

The statement is false.

Step by step solution

01

Given

dx鈫�dt=Ax鈫�

02

Explanation of the solution

Consider the given statement as follows.

If the trace and the determinant of a 3脳3matrixA are both negative, then the origin is stable equilibrium solution of the system as follows.

dx鈫�dt=Ax鈫�

It is given that the system isdx鈫�dt=Ax鈫� stable if and only if the trace is less than 0 and the determinant is greater than zero.

Since, the system is stable and as follows.

tr鈥�A<0and dt鈥�A>0.

Hence, the given statement is false.

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