Define a real valued function B on ℝ2 × ℝ2 as follows. If v = (x1, x2), w = (y1, y2) belong to ℝ2 define B(u, w) = x1y1 – x1y2 – x2y1 + 4x2y2. Let v0 = (1, 0) and let W = {v ∈ ℝ2 : B (v0, v) = 0}. Then W
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is not a subspace of ℝ2
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equals {(0, 0)}
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is the y axis
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is the line passing through (0, 0) and (1, 1)
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