this might be a stupid question,but if V=R^2 and S={(x_1,x_2):2x_1-3x_2=1}, then S is not a subspace of V since (0,0) is not in S, right?
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Looks good to me
If both x1 and x2 were zero, that (the zero vector) would not be in S. So you're right. Since zero does not equal one.
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