Endomorphism/Lines/Axes/Exercise

We consider the vectors ${}u={\begin{pmatrix}8\\7\\4\end{pmatrix}}$ and ${}v={\begin{pmatrix}6\\3\\9\end{pmatrix}}$ in ${}\mathbb {R} ^{3}$. Determine the dimension of the vector space, consisting of all linear mappings

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

that send ${}u$ to the ${}x$-axis and ${}v$ to the ${}y$-axis. Describe the corresponding linear subspace of the space of matrices with respect to suitable chosen bases.

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