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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College Algebra Graphs and Models
Authors: Marvin L. Bittinger, Judith A. Beecher, David J. Ellenbogen, Judith A. Penna
5th edition
321845404, 978-0321791009, 321791002, 978-0321783950, 321783956, 978-0321845405
