Linear mapping/Kernel and fiber/1/Exercise

Let

$\varphi \colon \mathbb {R} ^{3}\longrightarrow \mathbb {R} ,{\begin{pmatrix}x\\y\\z\end{pmatrix}}\longmapsto 4x-6y+9z.$

Determine, for the set

${}E={\left\{Q\in \mathbb {R} ^{3}\mid \varphi (Q)=5\right\}}\,,$

a description using a starting point and a translation space.

Create a solution