Answered: 1. Prove that each of the following…

1. Prove that each of the following sets is not a subspace. (i) W₁ = {A Є M2×2 | det(A) = 0} (ii) W₂ = {ƒ Є F(R,R) | ƒ(x) ≥ 0 for all x Є R}

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.2: Vector Spaces

Problem 43E: Prove that in a given vector space V, the zero vector is unique.

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Question

1. Prove that each of the following sets is not a subspace.
(i) W₁ = {A Є M2×2 | det(A) = 0}
(ii) W₂ = {ƒ Є F(R,R) | ƒ(x) ≥ 0 for all x Є R}

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