Below is a seven-step proof of the following theorem. Specify which of the ten vector space axioms applies. Theorem: Let u be any vector in a vector space V, let O be the zero vector in V, and let k be a scalar. Then k0=0. Proof: Reasons: (1) k0+ ku k(0+u) (2) - ku (3) Since ku is in V, -ku is in V. (4) Therefore, (k0+ku) + (-ku) ku + (-ku). Add ku to both sides (5) k0+ (ku+(-ku))-ku + (-ku) (6) k0+0=0 (7) k0=0

Below is a seven-step proof of the following theorem. Specify which of the ten vector space axioms applies. Theorem: Let u be any vector in a vector space V, let O be the zero vector in V, and let k be a scalar. Then k0=0. Proof: Reasons: (1) k0+ ku k(0+u) (2) - ku (3) Since ku is in V, -ku is in V. (4) Therefore, (k0+ku) + (-ku) ku + (-ku). Add ku to both sides (5) k0+ (ku+(-ku))-ku + (-ku) (6) k0+0=0 (7) k0=0

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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