Suppose $V=\Bbb{R}^3$ and $W=\Bbb{R}^2$.
Let $f:V\to W$ such that $f(x,y,z)=(zx+z,3y)$.
Find matrix $A$ of $f$ with respect to the standard bases of $V$ and $W$?
Suppose $V=\Bbb{R}^3$ and $W=\Bbb{R}^2$.
Let $f:V\to W$ such that $f(x,y,z)=(zx+z,3y)$.
Find matrix $A$ of $f$ with respect to the standard bases of $V$ and $W$?
As Martini already commented, $f$ cannot be represented by a matrix as it is not a linear map between $\mathbb R^3$ and $\mathbb R^2$.
So either you choose this as your answer to your question or else check the question carefully to verify the given $f$ is what you gave.
Quick proof of non-linearity: $f(1,1,1)=(2,3)$$f(2,2,2)=(6,6)\neq (4,6)=2f(1,1,1)$