Linear mapping/Kernel and fiber/2/Exercise

Let

$\varphi \colon \mathbb {R} ^{3}\longrightarrow \mathbb {R} ^{2},{\begin{pmatrix}x\\y\\z\end{pmatrix}}\longmapsto {\begin{pmatrix}7x+y-3z\\4x+5y\end{pmatrix}}.$

Determine, for the set

${}E={\left\{Q\in \mathbb {R} ^{3}\mid \varphi (Q)={\begin{pmatrix}4\\-2\end{pmatrix}}\right\}}\,,$

a description using a starting point and a translating space.

Create a solution