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).

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Linear Transformations
Section6.3: Matrices For Linear Transformations
Problem 52E: Let T be a linear transformation T such that T(v)=kv for v in Rn. Find the standard matrix for T.
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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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