Associated matrix with respect of a basis Given the following linear transformation:
$$f : \mathbb{R}^2 \to \mathbb{R}^3 | f(1; 0) = (1; 1; 0), f(0; 1)=(0; 1; 1)$$
find the associated matrix of $f$ with respect of the following basis:
$R = ((1; 0); (0; 1))$ of $\mathbb{R}^2$
and
$R^1 =
((1; 0; 0); (1; 1; 0); (0; 1; 1))$ of $\mathbb{R}^3$
--
I've found the associated matrix of $f$ with respect of the basis $R$, and it appears to be the following:
$$
\begin{bmatrix}1&0\\1&1\\0&1\end{bmatrix}
$$
Is it correct? How can I calculate the associated matrix of $f$ with respect of the basis $R^1$?

Assuming your associated Matrix is with respect to $R$ and the standart basis of $\mathbb{R}^3$, it is correct. But your associated Matrix is always depending on both bases of your vector spaces.
As $f(1;0)=0\cdot(1;0;0)+1\cdot(1;1;0)+0\cdot (0;1;1)$  
and $f(0;1)=0\cdot(1;0;0)+0\cdot(1;1;0)+1\cdot(0;1;1)$  
your Matrix with respect to $R,R^1$ is     $\begin{pmatrix}0&0\\1&0\\0&1\end{pmatrix}$
