Let T: R → R³ be given by (d) Find the eigenvectors of T. (e) Show that T is diagonalisable and write down the diagonal matrix D and the associated matrix P with PAP = D. (f) Check that AP = PD. %3D (g) Is T invertible?

Let T: R → R³ be given by (d) Find the eigenvectors of T. (e) Show that T is diagonalisable and write down the diagonal matrix D and the associated matrix P with PAP = D. (f) Check that AP = PD. %3D (g) Is T invertible?

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter5: Orthogonality

Section5.4: Orthogonal Diagonalization Of Symmetric Matrices

Problem 27EQ

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Let T: R → R³ be given by
(d) Find the eigenvectors of T.
(e) Show that T is diagonalisable and write down the diagonal matrix D and the associated matrix
P with PAP = D.
(f) Check that AP = PD.
%3D
(g) Is T invertible?

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