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

Let ${}E\subseteq \mathbb {R} ^{3}$ be the plane defined by the linear equation ${}5x+7y-4z=0$. Determine a linear map

$\varphi \colon \mathbb {R} ^{2}\longrightarrow \mathbb {R} ^{3},$

such that the image of ${}\varphi$ is equal to ${}E$.

Create a solution