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.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.4: Linear Transformations

Problem 34EQ

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