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Suppose that V and W are vector spaces, and both T and S are linear transformations from V to W. Show that A = is a vector space. veV|T(V): =0 and S() =

Suppose that V and W are vector spaces, and both T and S are linear transformations from V to W. Show that A = is a vector space. veV|T(V): =0 and S() =

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.4: Linear Transformations
Problem 12EQ
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Please help prove showing that it's true for the four properties given:  

Suppose that V and W are vector spaces, and both T and S are linear transformations from V to W. Show that A = {v€ V|T(V) =Ổ and S(V)=0} is a vector space.
Transcribed Image Text:Suppose that V and W are vector spaces, and both T and S are linear transformations from V to W. Show that A = {v€ V|T(V) =Ổ and S(V)=0} is a vector space.
1. The sum of u and v, denoted by u + v, is in V. 2. u + v = v + u. 3. (u + v) + w = u + (v + w). 4. There is a zero vector 0 in V such that u + 0 = u.
Transcribed Image Text:1. The sum of u and v, denoted by u + v, is in V. 2. u + v = v + u. 3. (u + v) + w = u + (v + w). 4. There is a zero vector 0 in V such that u + 0 = u.
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