Consider the linear map T: Pn(R) → Pn (R) such that T(p(x)) = x·p'(x) for every p(x) = P₁ (R). Select all the correct options. 0, 1, 2,..., nare the eigenvalues of T The eigenspace associated to each eigenvalue X = iis span (x¹) For each eigenvalue, the algebraic and geometric multiplicities are equal Tis diagonalisable
Consider the linear map T: Pn(R) → Pn (R) such that T(p(x)) = x·p'(x) for every p(x) = P₁ (R). Select all the correct options. 0, 1, 2,..., nare the eigenvalues of T The eigenspace associated to each eigenvalue X = iis span (x¹) For each eigenvalue, the algebraic and geometric multiplicities are equal Tis diagonalisable
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter5: Orthogonality
Section5.3: The Gram-schmidt Process And The Qr Factorization
Problem 1BEXP
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![Consider the linear mapT: Pn(R) → P₂ (R) such that T (p(x)) = x - p'(x) for every p(x) = P₁ (R).
Select all the correct options.
0, 1, 2, ..., nare the eigenvalues of T
The eigenspace associated to each eigenvalue λ = i is span (x²)
For each eigenvalue, the algebraic and geometric multiplicities are equal
Tis diagonalisable](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff6974066-f94e-4209-85de-714365386239%2F042a5f07-41e4-4fc3-8b51-db3cf4292bf7%2Fa5kge39_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the linear mapT: Pn(R) → P₂ (R) such that T (p(x)) = x - p'(x) for every p(x) = P₁ (R).
Select all the correct options.
0, 1, 2, ..., nare the eigenvalues of T
The eigenspace associated to each eigenvalue λ = i is span (x²)
For each eigenvalue, the algebraic and geometric multiplicities are equal
Tis diagonalisable
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