Real plane/Linear mapping/Not injective/Rational restriction/Exercise

Give an example for a linear mapping

$\varphi \colon \mathbb {R} ^{2}\longrightarrow \mathbb {R} ^{2},$

which is not injective, but such that its restriction

$\mathbb {Q} ^{2}\longrightarrow \mathbb {R} ^{2}$

is injective.

Create a solution