Exercises for Question Type 6: Determining the type of eigenvalue given a phase portrait diagram

Question 1

The following question relates to the analysis of linear systems of differential equations in the form \frac{d x}{d t} = Ax, where x \in R^{2} and A is a 2 \times 2 real constant matrix.

A linear system of differential equations is represented by the phase portrait shown below: Draw on this Identify the type of equilibrium point at the origin and characterize the nature of the eigenvalues of the system matrix A .

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Question 2

This question involves the analysis of a phase portrait for a system of linear differential equations.

The following phase portrait shows the trajectories of a system of linear differential equations \frac{d x}{d t} = Ax near the origin. Draw on this Identify the nature of the eigenvalues of matrix A and the type of equilibrium point at the origin. Justify your answers.

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Question 3

This question tests the ability to qualitatively analyze a phase portrait of a system of linear differential equations \frac{d x}{d t} = Ax to identify the classification of an equilibrium point and the nature of the associated eigenvalues and eigenvectors.

The following phase portrait shows the trajectories of a system of linear differential equations \frac{d x}{d t} = Ax near an equilibrium point at the origin. Draw on this Classify the equilibrium point and describe the nature of the eigenvalues and eigenvectors of matrix A .

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Question 4

The following phase portrait represents the behavior of a linear system \dot{x} = A x in the plane.

Examine the following phase portrait: Draw on this Determine the equilibrium type at the origin and characterize the eigenvalues of the corresponding system.

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Question 5

Identify the type of equilibrium point and describe its eigenvalues based on the given phase portrait.

Consider the following phase portrait for a linear system of differential equations: Draw on this Identify the equilibrium type at the origin and describe the nature of the eigenvalues, λ, associated with this system.

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Question 6

Consider the following phase portrait for a system of linear differential equations: Draw on this Classify the equilibrium point at the origin and describe the nature of its corresponding eigenvalues.

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Question 7

Examine the following phase portrait: Draw on this Determine the type of equilibrium point at the origin and describe the characteristics of its eigenvalues.

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Question 8

The following phase portrait is given for a system of linear differential equations: Draw on this Classify the equilibrium at the origin and state the nature of its eigenvalues.

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Question 9

Determine the type of equilibrium and the nature of the eigenvalues from a given phase portrait.

Consider the phase portrait shown below: Draw on this Determine the type of equilibrium at the origin and describe the eigenvalues (real or complex, distinct or repeated, and sign).

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Question 10

Level: HL Paper: 2

Analyze the phase portrait shown below for a system of linear differential equations: Draw on this Identify the type of equilibrium point at the origin and describe the nature of its eigenvalues.

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Question 11

The diagram shows the phase portrait of a linear system of differential equations near the origin.

Identify the type of equilibrium point at the origin and describe the nature of its eigenvalues.

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IB Mathematics Applications & Interpretation Question Type 6: Determining the Type of Eigenvalue Given a Phase Portrait Diagram Exercises