- #1

TheRookie

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## Homework Statement

I'm a 2nd year undergraduate student, so I suppose many users here won't find this too difficult, but I've had some issues with the following questions and, of course, any help would be very much appreciated:

(i) Prove f: V→W is affine (where V and W are real vector space) iff it is of the form f(x) = Tx + b, where T: V→ W is linear and b∈W. Prove T and b are uniquely determined by f.

(ii) Prove the image of an affine subset under an affine mapping is affine. Prove the composition of two affine maps is affine.

## Homework Equations

## The Attempt at a Solution

(i) If f: V→W is an affine mapping, we must have f(λx + (1-λ)y) = λf(x) + (1-λ)f(y) for all x and y in V, and λ in ℝ.

This is what immediately came to mind, but I can't see a connection between this and the question...

(ii) I'm sorry, but I've gone over this again and again and don't know where to start.Regards,

Pete