2. Let T € L(R?) be defined by Tv = Av, where A is the matrix[2/V5[1/v5]orthonormal basis for R?.[-1/V5]2/V5(a) Show that v = Nais an eigenvector for T, and show that vị together with v2 =form an(b) Show that T is not self-adjoint.(c) Explain why the results of (a) and (b) do not violate the Real Spectral Theorem.

Given Tv=Av ; Where A=-54-45 a.) v1=2515 is an eigen vector for T if, Tv1=λT. Since, Tv=Av. Thus,…

2. Let T E L(R?) be defined by Tv = Av, where A is the matrix [2/V3] is an eigenvector for T, and show that vị together with vz = [1/V5 [-1/V5 2/V5 form an (a) Show that v = orthonormal basis for R?. (b) Show that T is not self-adjoint. (c) Explain why the results of (a) and (b) do not violate the Real Spectral Theorem.

2. Let T E L(R?) be defined by Tv = Av, where A is the matrix [2/V3] is an eigenvector for T, and show that vị together with vz = [1/V5 [-1/V5 2/V5 form an (a) Show that v = orthonormal basis for R?. (b) Show that T is not self-adjoint. (c) Explain why the results of (a) and (b) do not violate the Real Spectral Theorem.

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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