Question: A function T: V W between vector spaces V and W is called additive if T(x + y) = T(x) + T(y) for all x,

AfunctionT:VWbetweenvector spaces VandWis calledadditive ifT(x + y) = T(x) + T(y) for all x, y V.Provethatif VandWarevector spaces overthefieldofrational numbers,then any additive functionfromVintoWis alinear transformation.

My attempt to prove this would be to show that T(x) is closed under scalar multiplication because by definition then T would be linear, but I am not sure how to show this.

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