Let T: P2 (R) -› P2 (R) be a transformation defined as: T(f(x)) = f'(x) ∀ f(x) E P2 (R), and S: P1 (R) - P2 (R) be transformation defined as: S(g(x)) = xg(x) ∀ g(x) E P2 (R). Prove that S and T are linear transformations and also find the matrix representation of ToS w.r.t. standard bases a = (1,x,x^2} of P2(R) and ß = (1,x) of P1 (R), i.e., find [ToS] ß
Let T: P2 (R) -› P2 (R) be a transformation defined as: T(f(x)) = f'(x) ∀ f(x) E P2 (R), and S: P1 (R) - P2 (R) be transformation defined as: S(g(x)) = xg(x) ∀ g(x) E P2 (R). Prove that S and T are linear transformations and also find the matrix representation of ToS w.r.t. standard bases a = (1,x,x^2} of P2(R) and ß = (1,x) of P1 (R), i.e., find [ToS] ß
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Linear Transformations
Section6.1: Introduction To Linear Transformations
Problem 42E
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Let T: P2 (R) -› P2 (R) be a transformation defined as: T(f(x)) = f'(x) ∀ f(x) E P2 (R),
and S: P1 (R) - P2 (R) be transformation defined as: S(g(x)) = xg(x) ∀ g(x) E P2 (R).
Prove that S and T are linear transformations and also find the matrix representation of
ToS w.r.t. standard bases a = (1,x,x^2} of P2(R) and ß = (1,x) of P1 (R), i.e., find [ToS] ß
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