Affine space/Affine plane/Description as preimage/2/Exercise

Describe the affine plane

${}E={\left\{{\begin{pmatrix}5\\6\\-2\end{pmatrix}}+s{\begin{pmatrix}3\\-4\\8\end{pmatrix}}+t{\begin{pmatrix}5\\4\\7\end{pmatrix}}\mid s,t\in \mathbb {R} \right\}}\,$

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

Create a solution