Let B = {x2 + 2, x² - 4x + 7, -x + 1} be a basis for P2 and let B' = {x³ + x², x³ + x² + x, x + 1, x³ + 1} be a basis for P3. Let T: P3 → P2 be the linear transformation defined by 3r 2p(t) dt. T(p(x)) = (x + 1)p(x) + p′(1) + Find [T], the matrix representation of T with respect to the basis B of P2 and the basis B' of P3.

Let B = {x2 + 2, x² - 4x + 7, -x + 1} be a basis for P2 and let B' = {x³ + x², x³ + x² + x, x + 1, x³ + 1} be a basis for P3. Let T: P3 → P2 be the linear transformation defined by 3r 2p(t) dt. T(p(x)) = (x + 1)p(x) + p′(1) + Find [T], the matrix representation of T with respect to the basis B of P2 and the basis B' of P3.

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 25CM: Find a basis B for R3 such that the matrix for the linear transformation T:R3R3,...

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