Find the smallest operator T: R³ R³ integer value for K so that the linear 3 given by T(x,y,z) = (x+y+z‚kx + y −z₂x+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 canotic basis of the R³.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Find the smallest integer value for K so that the linear
,3
operator T:R°→R° given by
T(xy,z) = (x + y +z,kx +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 canotic basis of
the R
Transcribed Image Text:Find the smallest integer value for K so that the linear ,3 operator T:R°→R° given by T(xy,z) = (x + y +z,kx +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 canotic basis of the R
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