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## Homework Statement

Proof that any affine function can be written as [itex]f(x) = Ax + b[/itex], [itex]A \in \mathbb{R}^{m\times n}[/itex] and [itex]x,y \in \mathbb{R}^n[/itex], [itex]b \in \mathbb{R}^m[/itex]

## Homework Equations

Affine function: [itex]f(\alpha x + \beta y) = \alpha f(x) + \beta f(y)[/itex] with [itex]\alpha+\beta=1[/itex]

## The Attempt at a Solution

I could proof that the function f(x)=Ax + b is affine.

However, I am stuck proofing that

**any**affine function can be represented so.

Any pointer how I can start here?