5. Prove that (-1)v=-v for every vector v in a vector space.

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.2: Vector Spaces
Problem 44E: Prove that in a given vector space V, the additive inverse of a vector is unique.
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Do 5

2. Prove that every element in a vector
space has a unique additive inverse.
3. Prove that Ov=0 for every vector v in a
vector space.
4. Prove that a0=0 for every scalar a in a
vector space.
5. Prove that (-1)v=-v for every vector v in a
vector space.
Transcribed Image Text:2. Prove that every element in a vector space has a unique additive inverse. 3. Prove that Ov=0 for every vector v in a vector space. 4. Prove that a0=0 for every scalar a in a vector space. 5. Prove that (-1)v=-v for every vector v in a vector space.
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