Solution-Determining the vector spaces

Determining the vector spaces

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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, y ∈V. Prove that if V and W are vector spaces over the field of rational numbers, then any additive function from V into W is a linear 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.

Reference no: EM131397419

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Determining the vector spaces : 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, y ∈V. Prove that if V and W are vector spaces over the field of rational numbers, then any additive function from V into W is a linear transform..

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Determining the vector spaces

Reference no: EM131397419

Reference no: EM131397419

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