1. Based on the axioms of a vector space V over a field F prove the following: (a) If x, y z ¤ V and x+y=z+y then x = y. (b) The additive inverse of any vector x in V is obtained through multiplication of x by the scalar (-1). Indicate what axiom(s) are used in each step.

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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1. Based on the axioms of a vector space V over a field F prove the following:
(a) If x, y z ¤ V and x + y = z + y then x = y.
(b) The additive inverse of any vector x in V is obtained through multiplication of x
by the scalar (-1).
Indicate what axiom(s) are used in each step.
Transcribed Image Text:1. Based on the axioms of a vector space V over a field F prove the following: (a) If x, y z ¤ V and x + y = z + y then x = y. (b) The additive inverse of any vector x in V is obtained through multiplication of x by the scalar (-1). Indicate what axiom(s) are used in each step.
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