let R^3 be a vector space with usual addition and scalar multiplication then
w=(x,y,z)€r^3/ x does not equal to y is
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(1) if v, w ∈ V then their vector sum v + w is in V and. • v + w ... The addition and scalar multiplication operations here are just the ones of R3, ... (so that x + y + z = 0) and then for r ∈ R observe that the scalar multiple r ·.
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