2. Let T: P₂ (R) → P₂(R) be defined by T(p)(x) = p(0) + p(1)(x+x²). (a) Prove that T is diagonalizable. (b) Find a basis D for P2 (R) such that [T]p is a diagonal matrix. Note that the basis D should consists of polynomials. (c) Compute [T]D (which should be a diagonal matrix).
2. Let T: P₂ (R) → P₂(R) be defined by T(p)(x) = p(0) + p(1)(x+x²). (a) Prove that T is diagonalizable. (b) Find a basis D for P2 (R) such that [T]p is a diagonal matrix. Note that the basis D should consists of polynomials. (c) Compute [T]D (which should be a diagonal matrix).
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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