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.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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