Find the smallest integer value for k such that the linear operator T:R3⟶R3 given by T(x,y,z)=(x+y+kz, x+y−z, x+y+z) is dagonalizable . Then for the value of k found, determine a diagonal matrix similar to the matrix of the operator T in the canonical basis of R3.

Find the smallest integer value for k such that the linear operator T:R3⟶R3 given by T(x,y,z)=(x+y+kz, x+y−z, x+y+z) is dagonalizable . Then for the value of k found, determine a diagonal matrix similar to the matrix of the operator T in the canonical basis of R3.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.6: Matrices

Problem 25E: Let A and B be square matrices of order n over Prove or disprove that the product AB is a diagonal...

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Question

Find the smallest integer value for k such that the linear operator T:R₃⟶R₃ given by T(x,y,z)=(x+y+kz, x+y−z, x+y+z) is dagonalizable . Then for the value of k found, determine a diagonal matrix similar to the matrix of the operator T in the canonical basis of R3.

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