Let T be the transformation T:{polynomials of degree < 4} → {polynomials of degree < 4} dp T(p) = (x – 1)- dæ' where the last term is describing the first derivative of the polynomial p. a) Is Ta linear transformation? If yes, write down a matrix representing T with basis {1, x, x2 , x³ , x4} for the input and output spaces. b) What is the kernel of the linear transformation?
Let T be the transformation T:{polynomials of degree < 4} → {polynomials of degree < 4} dp T(p) = (x – 1)- dæ' where the last term is describing the first derivative of the polynomial p. a) Is Ta linear transformation? If yes, write down a matrix representing T with basis {1, x, x2 , x³ , x4} for the input and output spaces. b) What is the kernel of the linear transformation?
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 12CM
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