To state: Whether the statement is true or false: “If the Jacobian matrix A = g ′ ( X 1 ) at a critical point of a plane autonomous system has positive trace and determinant, then the critical point X 1 is unstable.”

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Answer 1

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Chapter 11, Problem 6CR

To determine

To state: Whether the statement is true or false: “If the Jacobian matrix A=g′(X1) at a critical point of a plane autonomous system has positive trace and determinant, then the critical point X1 is unstable.”

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Answer 2

Question

Chapter 11, Problem 6CR

To determine

To state: Whether the statement is true or false: “If the Jacobian matrix A=g′(X1) at a critical point of a plane autonomous system has positive trace and determinant, then the critical point X1 is unstable.”

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Answer 3

Question

Chapter 11, Problem 6CR

To determine

To state: Whether the statement is true or false: “If the Jacobian matrix A=g′(X1) at a critical point of a plane autonomous system has positive trace and determinant, then the critical point X1 is unstable.”

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Answer 4

Question

Chapter 11, Problem 6CR

To determine

To state: Whether the statement is true or false: “If the Jacobian matrix A=g′(X1) at a critical point of a plane autonomous system has positive trace and determinant, then the critical point X1 is unstable.”

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Answer 5

Chapter 11, Problem 6CR

To determine

To state: Whether the statement is true or false: “If the Jacobian matrix A=g′(X1) at a critical point of a plane autonomous system has positive trace and determinant, then the critical point X1 is unstable.”

Answer 6

Chapter 11, Problem 6CR

To determine

To state: Whether the statement is true or false: “If the Jacobian matrix A=g′(X1) at a critical point of a plane autonomous system has positive trace and determinant, then the critical point X1 is unstable.”

Answer 7

Chapter 11, Problem 6CR

To determine

To state: Whether the statement is true or false: “If the Jacobian matrix A=g′(X1) at a critical point of a plane autonomous system has positive trace and determinant, then the critical point X1 is unstable.”

Answer 8

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Answer 11

Ch. 11.1 - Prob. 1E Ch. 11.1 - Prob. 2E Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E Ch. 11.1 - Prob. 6E Ch. 11.1 - Prob. 7E Ch. 11.1 - Prob. 8E Ch. 11.1 - Prob. 9E Ch. 11.1 - Prob. 10E

To state: Whether the statement is true or false: “If the Jacobian matrix A = g ′ ( X 1 ) at a critical point of a plane autonomous system has positive trace and determinant, then the critical point X 1 is unstable.”

Solution Summary: The author states that if the Jacobian matrix A=gprime (X_1) has positive trace and determinant, then the critical point is unstable.

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To state: Whether the statement is true or false: “If the Jacobian matrix A=g′(X1) at a critical point of a plane autonomous system has positive trace and determinant, then the critical point X1 is unstable.”

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Chapter 11 Solutions