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Prove that a subset W of a vector space; V is a subspace of V if and only if 0 W and ax

Chapter 1, Problem 18

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QUESTION:

Prove that a subset W of a vector space; V is a subspace of V if and only if 0 W and ax + y W whenever a F and x. y W

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QUESTION:

Prove that a subset W of a vector space; V is a subspace of V if and only if 0 W and ax + y W whenever a F and x. y W

ANSWER:

Step 1 of 3

Consider  is a subspace. It is given that  and also  and  then:

Thus,

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