Let R be the field of real number and {e1, e2} be the standard basis for R2 . Consider the linear operator τ ∈ L(R2) defined by τ(e1) = e1 + 2e2 , τ (e2) = 4e1 + 3e2 Find the minimal polynomial for τ and show that the rational canonical form for τ is (see image) What are the elementary divisors of τ.

Let R be the field of real number and {e1, e2} be the standard basis for R2 . Consider the linear operator τ ∈ L(R2) defined by τ(e1) = e1 + 2e2 , τ (e2) = 4e1 + 3e2 Find the minimal polynomial for τ and show that the rational canonical form for τ is (see image) What are the elementary divisors of τ.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Let R be the field of real number and {e₁, e₂} be the standard basis for R² . Consider the linear operator τ ∈ L(R²) defined by

τ(e₁) = e₁ + 2e_{2 ,}

τ (e₂) = 4e₁ + 3e₂

Find the minimal polynomial for τ and show that the rational canonical form for τ is

(see image)

What are the elementary divisors of τ.

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