Prove W = {(a, b) | a = -b} is a Subspace of R^2

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Prove W = {(a, b) | a = -b} is a Subspace of R^2
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you are such a good teacher! i just cant understand why a subset being non empty is the same as 0 being in the subset.

Americabeatz
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Thank you for doing so many examples. I think I understand it now.

VikSun
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Are there any examples for this in finite fields?

johnsecen
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You're Awsome Teacher!, I can now understand better vectorial subspace, Thank You.

cosovobas
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Hi teacher! Help, please...Prove that the set of vectors B={(a, 1, 1)} is a vector subspace?

josecarlos-zchy
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In your previous examples you plugged in an arbitrary number to prove that it's wrong. I plugged in X = (5, 6) Y = (1, 2)
and then did the vector addition but it proves it wrong. Could you please clarify this regarding closed vector addition?

GEhehloopf