# Homework Help: Proof affine function as matrix equation

1. Sep 28, 2013

### divB

1. The problem statement, all variables and given/known data

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

2. Relevant equations

Affine function: $f(\alpha x + \beta y) = \alpha f(x) + \beta f(y)$ with $\alpha+\beta=1$

3. 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?

2. Sep 28, 2013

### Dick

Define the function g(x)=f(x)-f(0) and try to prove g is linear.

3. Sep 28, 2013

### Ray Vickson

The word you want is 'prove', not proof. To prove something is to supply a proof.

Anyway, to start, apply your definition of "affine" to the case of $x \in \mathbb{R}^n$ and $y = 0 \in \mathbb{R}^n$.