To find the probabilities of all the different kinds of fixed points of the system x ˙ = A x , where A= ( a b c d ) . Suppose, we pick the entries a, b,c, d independently and at random, form a uniform distribution on the interval [ − 1 , 1 ] Concept Introduction: Av = λv , the desired straight line solution exists, if v is an eigen vector of A with corresponding eigen value λ In general, the eigen value of a matrix A is given by the characteristic equation det ( A-λI ) = 0 , where I is the identity matrix

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Answer 1

Question

Chapter 5.2, Problem 14E

Interpretation Introduction

Interpretation:

To find the probabilities of all the different kinds of fixed points of the system x˙=Ax, where A=(abcd). Suppose, we pick the entries a, b,c, d independently and at random, form a uniform distribution on the interval [−1,1]

Concept Introduction:

Av = λv, the desired straight line solution exists, if v is an eigen vector of A with corresponding eigen value λ

In general, the eigen value of a matrix A is given by the characteristic equation

det(A-λI) = 0, where I is the identity matrix

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Answer 2

Question

Chapter 5.2, Problem 14E

Interpretation Introduction

Interpretation:

To find the probabilities of all the different kinds of fixed points of the system x˙=Ax, where A=(abcd). Suppose, we pick the entries a, b,c, d independently and at random, form a uniform distribution on the interval [−1,1]

Concept Introduction:

Av = λv, the desired straight line solution exists, if v is an eigen vector of A with corresponding eigen value λ

In general, the eigen value of a matrix A is given by the characteristic equation

det(A-λI) = 0, where I is the identity matrix

Expert Solution & Answer

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Answer 3

Question

Chapter 5.2, Problem 14E

Interpretation Introduction

Interpretation:

To find the probabilities of all the different kinds of fixed points of the system x˙=Ax, where A=(abcd). Suppose, we pick the entries a, b,c, d independently and at random, form a uniform distribution on the interval [−1,1]

Concept Introduction:

Av = λv, the desired straight line solution exists, if v is an eigen vector of A with corresponding eigen value λ

In general, the eigen value of a matrix A is given by the characteristic equation

det(A-λI) = 0, where I is the identity matrix

Expert Solution & Answer

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Answer 4

Question

Chapter 5.2, Problem 14E

Interpretation Introduction

Interpretation:

To find the probabilities of all the different kinds of fixed points of the system x˙=Ax, where A=(abcd). Suppose, we pick the entries a, b,c, d independently and at random, form a uniform distribution on the interval [−1,1]

Concept Introduction:

Av = λv, the desired straight line solution exists, if v is an eigen vector of A with corresponding eigen value λ

In general, the eigen value of a matrix A is given by the characteristic equation

det(A-λI) = 0, where I is the identity matrix

Expert Solution & Answer

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Answer 5

Chapter 5.2, Problem 14E

Interpretation Introduction

Interpretation:

To find the probabilities of all the different kinds of fixed points of the system x˙=Ax, where A=(abcd). Suppose, we pick the entries a, b,c, d independently and at random, form a uniform distribution on the interval [−1,1]

Concept Introduction:

Av = λv, the desired straight line solution exists, if v is an eigen vector of A with corresponding eigen value λ

In general, the eigen value of a matrix A is given by the characteristic equation

det(A-λI) = 0, where I is the identity matrix

Answer 6

Chapter 5.2, Problem 14E

Interpretation Introduction

Interpretation:

To find the probabilities of all the different kinds of fixed points of the system x˙=Ax, where A=(abcd). Suppose, we pick the entries a, b,c, d independently and at random, form a uniform distribution on the interval [−1,1]

Concept Introduction:

Av = λv, the desired straight line solution exists, if v is an eigen vector of A with corresponding eigen value λ

In general, the eigen value of a matrix A is given by the characteristic equation

det(A-λI) = 0, where I is the identity matrix

Answer 7

Chapter 5.2, Problem 14E

Interpretation Introduction

Interpretation:

To find the probabilities of all the different kinds of fixed points of the system x˙=Ax, where A=(abcd). Suppose, we pick the entries a, b,c, d independently and at random, form a uniform distribution on the interval [−1,1]

Concept Introduction:

Av = λv, the desired straight line solution exists, if v is an eigen vector of A with corresponding eigen value λ

In general, the eigen value of a matrix A is given by the characteristic equation

det(A-λI) = 0, where I is the identity matrix

Answer 8

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Answer 9

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Answer 10

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Answer 11

Ch. 5.1 - Prob. 1E Ch. 5.1 - Prob. 2E Ch. 5.1 - Prob. 3E Ch. 5.1 - Prob. 4E Ch. 5.1 - Prob. 5E Ch. 5.1 - Prob. 6E Ch. 5.1 - Prob. 7E Ch. 5.1 - Prob. 8E Ch. 5.1 - Prob. 9E Ch. 5.1 - Prob. 10E

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