Is W a subspace of V? W=(x,y,2x-3y) V=R^3

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Is W a subspace of V? W=(x,y,2x-3y) V=R^3

Mathematics
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They are closed under addition:\[(x_1,y_1,2x_1-3y_1) +(x_2,y_2,2x_2-3y_2)\]\[=(x_1+x_2,y_1+y_2,2(x_1+x_2)-3(y_1+y_2))\]which is in W I'll let you verify that there is nothing to multiply it by that would take it out of W either, hence it is also closed under scalar multiplication
Thanks That was clear :D

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