Let S and T be linear maps of V on W. We define S + T as (S + T)v = S(v) + T(v) for all v ∈ V and we define aS as (aS)v = a*S(v) for all a ∈ R and v ∈ V. Judge the following statements as true or false: (a) X = {T; T: V → W} is not vector space. (b) S + T is a linear transformation from V into W. (c) aS is a linear transformation from V into W.

Let S and T be linear maps of V on W. We define S + T as (S + T)v = S(v) + T(v) for all v ∈ V and we define aS as (aS)v = a*S(v) for all a ∈ R and v ∈ V. Judge the following statements as true or false: (a) X = {T; T: V → W} is not vector space. (b) S + T is a linear transformation from V into W. (c) aS is a linear transformation from V into W.

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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