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Determine if the subset W={[x y]∈R2∣ x+y ≥0} is a subspace of R2.

Determine if the subset W={[x y]∈R2∣ x+y ≥0} is a subspace of R2.

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Answer #1

Solution:

A subspace of is a subset   of   satisfying:

Let   and   

Then  

But    as

is not a subspace of   .

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