3. Let TЄ L(C2) be a linear operator with only a single eigenvalue, λ = C. Show that p(T) = 0 € L(C²) for p(x) = (x − λ)². Hints: Remember that we cannot assume T is diagonalizable, and that we should not use determinants

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.9: Properties Of Determinants
Problem 34E
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3. Let TЄ L(C2) be a linear operator with only a single eigenvalue, λ = C. Show that
p(T) = 0 € L(C²) for p(x) = (x − λ)².
Hints: Remember that we cannot assume T is diagonalizable, and that we should not
use determinants
Transcribed Image Text:3. Let TЄ L(C2) be a linear operator with only a single eigenvalue, λ = C. Show that p(T) = 0 € L(C²) for p(x) = (x − λ)². Hints: Remember that we cannot assume T is diagonalizable, and that we should not use determinants
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