To prove: The non-homogenous linear system X ′ = A X + F has a unique critical point X 1 when Δ = det ( a ) ≠ 0 and also conclude that if X = X ( t ) is a solution to the non-homogenous system, then X ( t ) = X 1 .

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Answer 1

Question

Chapter 11.2, Problem 21E

To determine

To prove: The non-homogenous linear system X′=AX+F has a unique critical point X1 when Δ=det(a)≠0 and also conclude that if X=X(t) is a solution to the non-homogenous system, then X(t)=X1.

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Answer 2

Question

Chapter 11.2, Problem 21E

To determine

To prove: The non-homogenous linear system X′=AX+F has a unique critical point X1 when Δ=det(a)≠0 and also conclude that if X=X(t) is a solution to the non-homogenous system, then X(t)=X1.

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Answer 3

Question

Chapter 11.2, Problem 21E

To determine

To prove: The non-homogenous linear system X′=AX+F has a unique critical point X1 when Δ=det(a)≠0 and also conclude that if X=X(t) is a solution to the non-homogenous system, then X(t)=X1.

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Answer 4

Question

Chapter 11.2, Problem 21E

To determine

To prove: The non-homogenous linear system X′=AX+F has a unique critical point X1 when Δ=det(a)≠0 and also conclude that if X=X(t) is a solution to the non-homogenous system, then X(t)=X1.

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Answer 5

Chapter 11.2, Problem 21E

To determine

To prove: The non-homogenous linear system X′=AX+F has a unique critical point X1 when Δ=det(a)≠0 and also conclude that if X=X(t) is a solution to the non-homogenous system, then X(t)=X1.

Answer 6

Chapter 11.2, Problem 21E

To determine

To prove: The non-homogenous linear system X′=AX+F has a unique critical point X1 when Δ=det(a)≠0 and also conclude that if X=X(t) is a solution to the non-homogenous system, then X(t)=X1.

Answer 7

Chapter 11.2, Problem 21E

To determine

To prove: The non-homogenous linear system X′=AX+F has a unique critical point X1 when Δ=det(a)≠0 and also conclude that if X=X(t) is a solution to the non-homogenous system, then X(t)=X1.

Answer 8

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Answer 9

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Answer 10

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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 prove: The non-homogenous linear system X ′ = A X + F has a unique critical point X 1 when Δ = det ( a ) ≠ 0 and also conclude that if X = X ( t ) is a solution to the non-homogenous system, then X ( t ) = X 1 .

Solution Summary: The author evaluates the critical points of the non-homogenous linear system Xprime=AX+F by setting the RHS of differential equations equal to zero.

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To prove: The non-homogenous linear system X′=AX+F has a unique critical point X1 when Δ=det(a)≠0 and also conclude that if X=X(t) is a solution to the non-homogenous system, then X(t)=X1.

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Chapter 11 Solutions