The trace determinant plane in our textbook (and in We- bAssign) includes two border cases: (1) when τ = 0 (and ∆ > 0), we have a center point and (2) when τ 2 = 4∆, we have a degenerate node. It does not include the other border case when ∆ = 0. (c) Suppose τ > 0. Is the (0, 0) equilibrium stable or unstable in this case? What if τ < 0

The trace determinant plane in our textbook (and in We- bAssign) includes two border cases: (1) when τ = 0 (and ∆ > 0), we have a center point and (2) when τ 2 = 4∆, we have a degenerate node. It does not include the other border case when ∆ = 0. (c) Suppose τ > 0. Is the (0, 0) equilibrium stable or unstable in this case? What if τ < 0

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.2: Determinants

Problem 3AEXP

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The trace determinant plane in our textbook (and in We-bAssign) includes two border cases: (1) when τ = 0 (and ∆ > 0), wehave a center point and (2) when τ 2 = 4∆, we have a degenerate node.It does not include the other border case when ∆ = 0.(a) What type of eigenvalues do we have when ∆ = 0 (remember, wefound the eigenvalues in terms of τ and ∆ in HW10)