$\displaystyle h: {\mathbb{R} }^3 \rightarrow {\mathbb{R} }^2 $ is given by $\displaystyle h(x,y,z) =(7x, y-z) $ is a linear mapping.

For this function, write down its matrix with respect to the standard bases of the domain and codomain.

I took this to mean $\displaystyle h_A (\bold{x} ) = A \bold{x} = A \begin{bmatrix} x\\ y \\ z \\ \end{bmatrix} = \begin{bmatrix} 7x \\ y-z\\ \end {bmatrix} $

where $\displaystyle A = \begin{bmatrix} 7 & 0 & 0 \\ 0 & 1 & -1 \\ \end{bmatrix} $. But how do I write this down with respect to the standard bases of the domain and codomain. I know these are (1,0,0), (0,1,0), (0,0,1) , (1,0), (0,1). Thanks very much.