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11. Identify R+¹ with the set Pn of polynomials of degree ≤n, via the corre- spondence (An, . . . , Ao) ↔ Ant” + + ait + ao. Let D: P→ Pn be the differentiation operator. Prove D is nilpotent. 12. Find the matrix of D in the standard basis in Problem 11.

11. Identify R+¹ with the set Pn of polynomials of degree ≤n, via the corre- spondence (An, . . . , Ao) ↔ Ant” + + ait + ao. Let D: P→ Pn be the differentiation operator. Prove D is nilpotent. 12. Find the matrix of D in the standard basis in Problem 11.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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11. Identify R+1 with the set Pn of polynomials of degree ≤n, via the corre- spondence 12. (an, ao) → ant + + ait + ao. Let D: Pn → P₁ be the differentiation operator. Prove D is nilpotent. Find the matrix of D in the standard basis in Problem 11.
Transcribed Image Text:11. Identify R+1 with the set Pn of polynomials of degree ≤n, via the corre- spondence 12. (an, ao) → ant + + ait + ao. Let D: Pn → P₁ be the differentiation operator. Prove D is nilpotent. Find the matrix of D in the standard basis in Problem 11.
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