Affine space/Affine plane/Description as preimage/1/Exercise

Describe the affine plane

${}E={\left\{{\begin{pmatrix}3\\1\\4\end{pmatrix}}+s{\begin{pmatrix}2\\7\\-6\end{pmatrix}}+t{\begin{pmatrix}-1\\5\\1\end{pmatrix}}\mid s,t\in \mathbb {R} \right\}}\,$

as the preimage over ${}1$ of an affine mapping ${}\psi \colon \mathbb {R} ^{3}\rightarrow \mathbb {R}$.

Create a solution