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Consider the following system: k 2²-(33) ² = dt k= Find the eigenvalues in terms of k. (Enter your answer as a comma-separated list.) λ = When k = 4, determine the type of the equilibrium point at the origin. The origin is a(n) ? k Find the critical value or values of k at which the qualitative nature of the phase portrait changes. (If there is more than one such value, enter a comma-separated list.) Draw phase portraits for values of k slightly above and slightly below each of the critical values you found.

Consider the following system: k 2²-(33) ² = dt k= Find the eigenvalues in terms of k. (Enter your answer as a comma-separated list.) λ = When k = 4, determine the type of the equilibrium point at the origin. The origin is a(n) ? k Find the critical value or values of k at which the qualitative nature of the phase portrait changes. (If there is more than one such value, enter a comma-separated list.) Draw phase portraits for values of k slightly above and slightly below each of the critical values you found.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter5: Orthogonality
Section5.3: The Gram-schmidt Process And The Qr Factorization
Problem 1BEXP
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Consider the following system: dt I k = = Find the eigenvalues in terms of k. (Enter your answer as a comma-separated list.) λ = When k = 4, determine the type of the equilibrium point at the origin. The origin is a(n) ? k 3 I -3 k Find the critical value or values of k at which the qualitative nature of the phase portrait changes. (If there is more than one such value, enter a comma-separated list.) Draw phase portraits for values of k slightly above and slightly below each of the critical values you found.
Transcribed Image Text:Consider the following system: dt I k = = Find the eigenvalues in terms of k. (Enter your answer as a comma-separated list.) λ = When k = 4, determine the type of the equilibrium point at the origin. The origin is a(n) ? k 3 I -3 k Find the critical value or values of k at which the qualitative nature of the phase portrait changes. (If there is more than one such value, enter a comma-separated list.) Draw phase portraits for values of k slightly above and slightly below each of the critical values you found.
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