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

Algebra and Trigonometry (6th Edition)
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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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
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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