Let operator be T:R³ → R³ with correspondence rule T(x, y, z) = (y, x + z, 0) a) Determine the characteristic values of T. b) Obtain the characteristic spaces of T. c) Indicate whether A is diagonalizable and, if so, obtain the matrix P that diagonalizes A.

Let operator be T:R³ → R³ with correspondence rule T(x, y, z) = (y, x + z, 0) a) Determine the characteristic values of T. b) Obtain the characteristic spaces of T. c) Indicate whether A is diagonalizable and, if so, obtain the matrix P that diagonalizes A.

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 28EQ

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Question

Let operator be T: R³ → R³ with correspondence rule
T(х, у, 2) %3 (у, х +z,0)
a) Determine the characteristic values of T.
b) Obtain the characteristic spaces of T.
c) Indicate whether A is diagonalizable and, if so, obtain the matrix P that diagonalizes A.

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