Let P4 = set of polynomials with degree less than or equal to 4, and T: P4 → P4 f → f′ (derived), ie T(f)=f′. Judge the following statements as true or false (a) The subset of P4 defined by N = {T ∈ P4 | T(p(x)) = 0} is a vector subspace of P4. (b) T is not a linear transformation.

Let P4 = set of polynomials with degree less than or equal to 4, and T: P4 → P4 f → f′ (derived), ie T(f)=f′. Judge the following statements as true or false (a) The subset of P4 defined by N = {T ∈ P4 | T(p(x)) = 0} is a vector subspace of P4. (b) T is not a 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 6CM: Let T:R4R2 be the linear transformation defined by T(v)=Av, where A=[10100101]. Find a basis for a...

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Question

Let P4 = set of polynomials with degree less than or equal to 4, and

T: P4 → P4

f → f′ (derived), ie T(f)=f′.

Judge the following statements as true or false

(a) The subset of P4 defined by N = {T ∈ P4 | T(p(x)) = 0} is a vector subspace of P4.

(b) T is not a linear transformation.

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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