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Give an example of a non-linear affine transformation.

Is this exercise correct? Since a affine transformation is written as $f(x)=Ax+b$ where $A\in Gl(\mathbb{R},n)$ and $b\in \mathbb{R^n} $ isn't a linear function by definition ?

I thought every function that can be represented with a matrix multiplication is linear.

Then I thought that maybe if $A$ was a rotation matrix, or have an element like $e^θ$ that would make it non-linear ?

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1 Answers1

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Every affine transformation where $b \neq 0$ (in your notation) is not linear. This exercise should likely drive home the point that linear functions in the sense usually taught at school are not what we usually consider linear functions in linear algebra etc.

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