# linear algebra subspace

could anyone help me on this subspace test please. would be much appreciated thank you

Let (V,+, ·) be $R^3$ with the usual vector addition and scalar multiplication. For each of the following, either use the subspace test to show that the given $W$ is a subspace of (V,+, ·) or explain why $W$ is not a subspace.

$$W := \{w \in V \mid w . (1,-3, 2) = 1\}$$

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You have a plane with normal vector $(1,-3,2)$ through the point $(0,0,1)$ that does not pass through the origin, and hence is not a subspace of $\Bbb{R}^3$.