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() =
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.4: Spanning Sets And Linear Independence
Problem 74E: Let u, v, and w be any three vectors from a vector space V. Determine whether the set of vectors...
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Please help prove showing that it's true for the four properties given:

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.

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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