# Plane in space/5x+7y-4z/Image of linear mapping/Exercise

Let ${\displaystyle {}E\subseteq \mathbb {R} ^{3}}$ be the plane defined by the linear equation ${\displaystyle {}5x+7y-4z=0}$. Determine a linear map
${\displaystyle \varphi \colon \mathbb {R} ^{2}\longrightarrow \mathbb {R} ^{3}}$
such that the image of ${\displaystyle {}\varphi }$ is equal to ${\displaystyle {}E}$.