Consider the linear operator D : P3 (R) → P3 (R) defined via the deriva- tive: D (f) = f'. Find the matrix representation of this linear operator with respect to the basis B = (1, x, x², x³).

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.2: Norms And Distance Functions
Problem 33EQ
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Could you show an example of how to do this type of problem, but change basis B to something else?

Consider the linear operator D : P3 (R) → P3 (R) defined via the deriva-
tive: D (f) = f'. Find the matrix representation of this linear operator with respect
to the basis B = (1, x, x², x³).
Transcribed Image Text:Consider the linear operator D : P3 (R) → P3 (R) defined via the deriva- tive: D (f) = f'. Find the matrix representation of this linear operator with respect to the basis B = (1, x, x², x³).
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