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Let T: R5 → R5  be a linear operator whose characteristic polynomial is pT(x) = (x−3)3(x−5)2. Let V3 and V5 be the eigenspaces associated with eigenvalues ​​3 and 5, respectively. Judge each item below as true or false. (A) If dimV3 = 3 and dimV5 = 2, then there exists a basis of R5 such that the matrix of T in that basis is

Let T: R5 → R5  be a linear operator whose characteristic polynomial is pT(x) = (x−3)3(x−5)2. Let V3 and V5 be the eigenspaces associated with eigenvalues ​​3 and 5, respectively. Judge each item below as true or false. (A) If dimV3 = 3 and dimV5 = 2, then there exists a basis of R5 such that the matrix of T in that basis is

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.2: Exponents And Radicals
Problem 46E
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Let T: R5 → R5  be a linear operator whose characteristic polynomial is pT(x) = (x−3)3(x−5)2. Let V3 and V5 be the eigenspaces associated with eigenvalues ​​3 and 5, respectively. Judge each item below as true or false.

(A) If dimV3 = 3 and dimV5 = 2, then there exists a basis of R5 such that the matrix of T in that basis is

 

3 0 0 0 0 3 0 0 3 0 0 5 0 0 5
Transcribed Image Text:3 0 0 0 0 3 0 0 3 0 0 5 0 0 5
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