Find the smallest internal value for k so that the linear operator T: R°→R° given by T(x,y,z) = (x +y+ kz,x + y – z,x + y +z) be degonalizable. Then, for the value of k found, determine a diagonal matrix similar to the matrix of the operator T on the canonical basis 3 of R3

Find the smallest internal value for k so that the linear operator T: R°→R° given by T(x,y,z) = (x +y+ kz,x + y – z,x + y +z) be degonalizable. Then, for the value of k found, determine a diagonal matrix similar to the matrix of the operator T on the canonical basis 3 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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Question

Find the smallest internal value for k so that the linear
operator T: R°→R° given by
T(x,y,z) = (x +y + kz,x + y – z,t + y +z) be degonalizable.
Then, for the value of k found, determine a diagonal matrix
similar to the matrix of the operator T on the canonical basis
of R.
3
.3

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