Consider $V= \left \{ v= \begin{bmatrix}
x\_1\\ 
x\_2\\ 
x\_3
\end{bmatrix} : x\_1-x\_2+2x\_3=0\right \}\subset K^3$ and the linear map $f:V \rightarrow K^2$ defined by

$f\begin{pmatrix}
x\_1\\ 
x\_2\\ 
x\_3
\end{pmatrix}=\begin{pmatrix}
x\_1-x\_3\\ 
x\_2-3x\_3
\end{pmatrix}$

Now, what is the matrix $M$ that represents $f:V \rightarrow K^2$ with respect to the basis of $V$ and the standard basis $(e\_1,e\_2)$ for $K^2$.

**So far**

I found the basis of V of dimension 2 to be the vectors ${(1, 1, 0), (-2, 0, 1)}$. But then I do not know how to continue. Maybe coordinate shift?