Find the smallest integer value for K so that the linear operator T: R→R such that T(x,y,z) = (3x + (1+ k)y, 3y, — ky +z) be diagonalizable. Then, for the value of K found, determine the diagonal matrix similar to the matrix of the operator T on the canonical basis of R³.
Find the smallest integer value for K so that the linear operator T: R→R such that T(x,y,z) = (3x + (1+ k)y, 3y, — ky +z) be diagonalizable. Then, for the value of K found, determine the diagonal matrix similar to the matrix of the operator T on the canonical basis of R³.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section: Chapter Questions
Problem 17RQ
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