. Prove that Ts is a linear transformation for all s b.Write down the representing matrix of Ts with respect to the ordered basis{s,x,x2) c.Prove that Ts is diagonalizable for all s (s0) and give all its eigenvalues.

. Prove that Ts is a linear transformation for all s b.Write down the representing matrix of Ts with respect to the ordered basis{s,x,x2) c.Prove that Ts is diagonalizable for all s (s0) and give all its eigenvalues.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter7: Eigenvalues And Eigenvectors

Section7.CR: Review Exercises

Problem 16CR

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Question

each s exists R

Ts(p(x))=sp(x)+(s+x)p'(x)+(s+x²)p''(x)

a. Prove that Ts is a linear transformation for all s

b.Write down the representing matrix of Ts with respect to the ordered basis{s,x,x²)

c.Prove that Ts is diagonalizable for all s (s0) and give all its eigenvalues.

d.Find a basis of R2[x] formed by eigenvector

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