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).
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.CM: Cumulative Review
Problem 18CM
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